6131:. In contrast to the macrostate, which characterizes plainly observable average quantities, a microstate specifies all molecular details about the system including the position and momentum of every molecule. The more such states are available to the system with appreciable probability, the greater the entropy. In statistical mechanics, entropy is a measure of the number of ways a system can be arranged, often taken to be a measure of "disorder" (the higher the entropy, the higher the disorder). This definition describes the entropy as being proportional to the natural logarithm of the number of possible microscopic configurations of the individual atoms and molecules of the system (
6964:
10562:
10298:. The traditional qualitative description of entropy is that it refers to changes in the state of the system and is a measure of "molecular disorder" and the amount of wasted energy in a dynamical energy transformation from one state or form to another. In this direction, several recent authors have derived exact entropy formulas to account for and measure disorder and order in atomic and molecular assemblies. One of the simpler entropy order/disorder formulas is that derived in 1984 by thermodynamic physicist Peter Landsberg, based on a combination of
12100:. Recent work has cast some doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly, moving the universe further from the heat death with time, not closer. This results in an "entropy gap" pushing the system further away from the posited heat death equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic
7370:, for example, may cool the air in a room, thus reducing the entropy of the air of that system. The heat expelled from the room (the system), which the air conditioner transports and discharges to the outside air, always makes a bigger contribution to the entropy of the environment than the decrease of the entropy of the air of that system. Thus, the total of entropy of the room plus the entropy of the environment increases, in agreement with the second law of thermodynamics.
8171:
17670:
100:
17557:
1670:
17581:
7533:, so that entropy density is locally defined as an intensive quantity. For such systems, there may apply a principle of maximum time rate of entropy production. It states that such a system may evolve to a steady state that maximizes its time rate of entropy production. This does not mean that such a system is necessarily always in a condition of maximum time rate of entropy production; it means that it may evolve to such a steady state.
6953:
17593:
7696:, implying that the internal energy is fixed when one specifies the entropy and the volume, this relation is valid even if the change from one state of thermal equilibrium to another with infinitesimally larger entropy and volume happens in a non-quasistatic way (so during this change the system may be very far out of thermal equilibrium and then the whole-system entropy, pressure, and temperature may not exist).
17569:
3621:. The classical approach defines entropy in terms of macroscopically measurable physical properties, such as bulk mass, volume, pressure, and temperature. The statistical definition of entropy defines it in terms of the statistics of the motions of the microscopic constituents of a system â modeled at first classically, e.g. Newtonian particles constituting a gas, and later quantum-mechanically (photons,
3843:, while the heat flow from a hot reservoir to a cold reservoir represents the increase in the entropy in a cold reservoir, the work output, if reversibly and perfectly stored, represents the decrease in the entropy which could be used to operate the heat engine in reverse, returning to the initial state; thus the total entropy change may still be zero at all times if the entire process is reversible.
4881:
10566:
3296:
10564:
10569:
10568:
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10570:
7097:, occurs when two or more different substances are mixed. If the substances are at the same temperature and pressure, there is no net exchange of heat or work â the entropy change is entirely due to the mixing of the different substances. At a statistical mechanical level, this results due to the change in available volume per particle with mixing.
10894:. A simple but important result within this setting is that entropy is uniquely determined, apart from a choice of unit and an additive constant for each chemical element, by the following properties: it is monotonic with respect to the relation of adiabatic accessibility, additive on composite systems, and extensive under scaling.
10567:
4726:
7347:
body without the application of work to the colder body. Secondly, it is impossible for any device operating on a cycle to produce net work from a single temperature reservoir; the production of net work requires flow of heat from a hotter reservoir to a colder reservoir, or a single expanding reservoir undergoing
4335:
10610:
internal portions at different temperatures tend to adjust to a single uniform temperature and thus produce equilibrium. A recently developed educational approach avoids ambiguous terms and describes such spreading out of energy as dispersal, which leads to loss of the differentials required for work
8358:
of the system at the point of the heat flow. If there are mass flows across the system boundaries, they also influence the total entropy of the system. This account, in terms of heat and work, is valid only for cases in which the work and heat transfers are by paths physically distinct from the paths
8137:
estimated the world's technological capacity to store and communicate optimally compressed information normalized on the most effective compression algorithms available in the year 2007, therefore estimating the entropy of the technologically available sources. The author's estimate that human kind's
7014:
from the warm surroundings spread to the cooler system of ice and water. Over time the temperature of the glass and its contents and the temperature of the room become equal. In other words, the entropy of the room has decreased as some of its energy has been dispersed to the ice and water, of which
11984:
change in temperature is recorded, until the temperature reaches a desired value (usually 25°C). The obtained data allows the user to integrate the equation above, yielding the absolute value of entropy of the substance at the final temperature. This value of entropy is called calorimetric entropy.
7346:
requires that, in general, the total entropy of any system does not decrease other than by increasing the entropy of some other system. Hence, in a system isolated from its environment, the entropy of that system tends not to decrease. It follows that heat cannot flow from a colder body to a hotter
7081:
must increase or remain constant. Therefore, entropy is not a conserved quantity: for example, in an isolated system with non-uniform temperature, heat might irreversibly flow and the temperature become more uniform such that entropy increases. Chemical reactions cause changes in entropy and system
6971:
for steam. The vertical axis represents uniform temperature, and the horizontal axis represents specific entropy. Each dark line on the graph represents constant pressure, and these form a mesh with light gray lines of constant volume. (Dark-blue is liquid water, light-blue is liquid-steam mixture,
11451:
In the case of transmitted messages, these probabilities were the probabilities that a particular message was actually transmitted, and the entropy of the message system was a measure of the average size of information of a message. For the case of equal probabilities (i.e. each message is equally
7022:
such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. Thus, when the "universe" of the room and ice water system has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. The
6127:, which remains about a system after its observable macroscopic properties, such as temperature, pressure and volume, have been taken into account. For a given set of macroscopic variables, the entropy measures the degree to which the probability of the system is spread out over different possible
4337:
To derive the Carnot efficiency Kelvin had to evaluate the ratio of the work output to the heat absorbed during the isothermal expansion with the help of the CarnotâClapeyron equation, which contained an unknown function called the Carnot function. The possibility that the Carnot function could be
3846:
In contrast, irreversible process increases the total entropy of the system and surroundings. Any process that happens quickly enough to deviate from the thermal equilibrium cannot be reversible, the total entropy increases, and the potential for maximum work to be done during the process is lost.
3388:
objected to the supposition that no change occurs in the working body, and gave that change a mathematical interpretation, by questioning the nature of the inherent loss of usable heat when work is done, e.g., heat produced by friction. He described his observations as a dissipative use of energy,
11983:
The process of measurement goes as follows. First, a sample of the substance is cooled as close to absolute zero as possible. At such temperatures, the entropy approaches zero – due to the definition of temperature. Then, small amounts of heat are introduced into the sample and the
12088:
have shown that black holes have the maximum possible entropy of any object of equal size. This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps. However, the escape of energy from black holes might be possible due to quantum
11270:
I thought of calling it "information", but the word was overly used, so I decided to call it "uncertainty". Von
Neumann told me, "You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a
10642:
of a particular quantity of energy. Energy supplied at a higher temperature (i.e. with low entropy) tends to be more useful than the same amount of energy available at a lower temperature. Mixing a hot parcel of a fluid with a cold one produces a parcel of intermediate temperature, in which the
5087:
5928:
To find the entropy difference between any two states of the system, the integral must be evaluated for some reversible path between the initial and final states. Since an entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path
12043:
Entropy has been proven useful in the analysis of base pair sequences in DNA. Many entropy-based measures have been shown to distinguish between different structural regions of the genome, differentiate between coding and non-coding regions of DNA, and can also be applied for the recreation of
11908:
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One dictionary definition of entropy is that it is "a measure of thermal energy per unit temperature that is not available for useful work" in a cyclic process. For instance, a substance at uniform temperature is at maximum entropy and cannot drive a heat engine. A substance at non-uniform
3653:
of other state variables. Often, if some properties of a system are determined, they are sufficient to determine the state of the system and thus other properties' values. For example, temperature and pressure of a given quantity of gas determine its state, and thus also its volume via the
6737:
of a system maximizes the entropy because it does not reflect all information about the initial conditions, except for the conserved variables. This uncertainty is not of the everyday subjective kind, but rather the uncertainty inherent to the experimental method and interpretative model.
4641:
5690:). This relationship was expressed in an increment of entropy that is equal to incremental heat transfer divided by temperature. Entropy was found to vary in the thermodynamic cycle but eventually returned to the same value at the end of every cycle. Thus it was found to be a
14974:
Inked page forms pattern w/ information â page entropy < diff page w/ randomized letters. Reduced entropy trivial compared to inked paper entropy. If the paper is burned, it hardly matters in a thermodynamic context if the text contains the meaning of life or only
6741:
The interpretative model has a central role in determining entropy. The qualifier "for a given set of macroscopic variables" above has deep implications when two observers use different sets of macroscopic variables. For example, consider observer A using variables
10306:
arguments. He argues that when constraints operate on a system, such that it is prevented from entering one or more of its possible or permitted states, as contrasted with its forbidden states, the measure of the total amount of "disorder" in the system is given
3262:
explained entropy as the measure of the number of possible microscopic arrangements or states of individual atoms and molecules of a system that comply with the macroscopic condition of the system. He thereby introduced the concept of statistical disorder and
4198:
3350:. Carnot based his views of heat partially on the early 18th-century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, and partially on the contemporary views of
12685:
the entropy of a body, after the Greek word 'transformation'. I have designedly coined the word entropy to be similar to 'energy', for these two quantities are so analogous in their physical significance, that an analogy of denomination seemed to me
7971:
7743:
independent of the size, as a specific entropy characteristic of the type of system studied. Specific entropy may be expressed relative to a unit of mass, typically the kilogram (unit: Jâ
kgâ
K). Alternatively, in chemistry, it is also referred to one
5430:
12602:
möglichst Àhnlich gebildet, denn die beiden Gröƿsen, welche durch diese Worte benannt werden sollen, sind ihren physikalischen
Bedeutungen nach einander so nahe verwandt, daƿs eine gewisse Gleichartigkeit in der Benennung mir zweckmÀƿsig zu seyn
11012:
6489:
12585:
des Körpers. Da ich es aber fĂŒr besser halte, die Namen derartiger fĂŒr die
Wissenschaft wichtiger Gröƿsen aus den alten Sprachen zu entnehmen, damit sie unverÀndert in allen neuen Sprachen angewandt werden können, so schlage ich vor, die Gröƿse
4442:
7521:
Statistical mechanics demonstrates that entropy is governed by probability, thus allowing for a decrease in disorder even in an isolated system. Although this is possible, such an event has a small probability of occurring, making it unlikely.
8507:
is generated within the system. For an open thermodynamic system in which heat and work are transferred by paths separate from the paths for transfer of matter, using this generic balance equation, with respect to the rate of change with time
9786:, the entropy change of any process in which temperature and volume both vary is the same as for a path divided into two steps â heating at constant volume and expansion at constant temperature. For an ideal gas, the total entropy change is:
4959:
5556:, could be analyzed from the same standpoint. Notably, any machine or cyclic process converting heat into work (i.e., heat engine) what is claimed to produce an efficiency greater than the one of Carnot is not viable â due to violation of
3354:, who showed in 1789 that heat could be created by friction, as when cannon bores are machined. Carnot reasoned that if the body of the working substance, such as a body of steam, is returned to its original state at the end of a complete
11798:
10108:
5328:
4643:
Since this equality holds over an entire Carnot cycle, it gave
Clausius the hint that at each stage of the cycle the difference between a work and a net heat would be conserved, rather than a net heat itself. Which means there exists a
10225:
8551:
6112:. In short, the thermodynamic definition of entropy provides the experimental verification of entropy, while the statistical definition of entropy extends the concept, providing an explanation and a deeper understanding of its nature.
4876:{\displaystyle {\frac {\left\vert Q_{\mathsf {H}}\right\vert }{T_{\mathsf {H}}}}-{\frac {\left\vert Q_{\mathsf {C}}\right\vert }{T_{\mathsf {C}}}}={\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}+{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}=0}
1892:
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9880:
6679:
is the number of microstates whose energy equals to the one of the system. Usually, this assumption is justified for an isolated system in a thermodynamic equilibrium. Then in case of an isolated system the previous formula reduces
4519:
6107:
in the 1870s by analyzing the statistical behavior of the microscopic components of the system. Boltzmann showed that this definition of entropy was equivalent to the thermodynamic entropy to within a constant factorâknown as the
5709:
flow to and from an isolated system, but energy flow to and from a closed system is possible. Nevertheless, for both closed and isolated systems, and indeed, also in open systems, irreversible thermodynamics processes may occur.
12052:
Assuming that a finite universe is an isolated system, the second law of thermodynamics states that its total entropy is continually increasing. It has been speculated, since the 19th century, that the universe is fated to a
3596:
Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension.
9207:
is never a known quantity but always a derived one based on the expression above. Therefore, the open system version of the second law is more appropriately described as the "entropy generation equation" since it specifies
10565:
10381:
10454:
10574:
Slow motion video of a glass cup smashing on a concrete floor. In the very short time period of the breaking process, the entropy of the mass making up the glass cup rises sharply, as the matter and energy of the glass
9460:
7731:
introduces the measurement of entropy change which describes the direction and quantifies the magnitude of simple changes such as heat transfer between systems â always from hotter body to cooler one spontaneously.
4955:
In addition, the total change of entropy in both thermal reservoirs over Carnot cycle is zero too, since the inversion of a heat transfer direction means a sign inversion for the heat transferred during isothermal
1962:
9989:
occur at constant temperature and pressure. The reversible heat is the enthalpy change for the transition, and the entropy change is the enthalpy change divided by the thermodynamic temperature. For fusion (i.e.,
5538:
6395:
7243:
5915:
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9741:
7674:
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The entropy of a system depends on its internal energy and its external parameters, such as its volume. In the thermodynamic limit, this fact leads to an equation relating the change in the internal energy
11438:
6076:
of that energy must be given up to the system's surroundings as a heat. Otherwise, this process cannot go forward. In classical thermodynamics, the entropy of a system is defined if and only if it is in a
11223:
9634:
7185:
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5771:
11608:
3625:, spins, etc.). The two approaches form a consistent, unified view of the same phenomenon as expressed in the second law of thermodynamics, which has found universal applicability to physical processes.
8779:
11455:
Most researchers consider information entropy and thermodynamic entropy directly linked to the same concept, while others argue that they are distinct. Both expressions are mathematically similar. If
7321:
Furthermore, it has been shown that the definitions of entropy in statistical mechanics is the only entropy that is equivalent to the classical thermodynamics entropy under the following postulates:
14992:
Schneider, Tom, DELILA system (Deoxyribonucleic acid
Library Language), (Information Theory Analysis of binding sites), Laboratory of Mathematical Biology, National Cancer Institute, Frederick, MD.
6922:
and its influence on the system. In other words, one must choose a complete set of macroscopic variables to describe the system, i.e. every independent parameter that may change during experiment.
1389:
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at a particular uniform temperature and pressure is determined, and is thus a particular state, and has a particular volume. The fact that entropy is a function of state makes it useful. In the
11793:
4166:
done by a reversible heat engine was found to be the product of the Carnot efficiency (i.e., the efficiency of all reversible heat engines with the same pair of thermal reservoirs) and the heat
7839:
7314:. However, the equivalence between the Gibbs entropy formula and the thermodynamic definition of entropy is not a fundamental thermodynamic relation but rather a consequence of the form of the
5829:
13492:
Gao, Xiang; Gallicchio, Emilio; Roitberg, Adrian (2019). "The generalized
Boltzmann distribution is the only distribution in which the Gibbs-Shannon entropy equals the thermodynamic entropy".
5353:
4710:
9256:
7308:
3419:, that heat was an indestructible particle that had mass. Clausius discovered that the non-usable energy increases as steam proceeds from inlet to exhaust in a steam engine. From the prefix
10923:
8425:
6724:
6400:
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7062:. Increases in the total entropy of system and surroundings correspond to irreversible changes, because some energy is expended as waste heat, limiting the amount of work a system can do.
9055:
3239:, one of the leading founders of the field of thermodynamics, defined it as the quotient of an infinitesimal amount of heat to the instantaneous temperature. He initially described it as
2648:
12665:: "I prefer going to the ancient languages for the names of important scientific quantities, so that they may mean the same thing in all living tongues. I propose, accordingly, to call
7699:
The fundamental thermodynamic relation implies many thermodynamic identities that are valid in general, independent of the microscopic details of the system. Important examples are the
10268:
In
Boltzmann's analysis in terms of constituent particles, entropy is a measure of the number of possible microscopic states (or microstates) of a system in thermodynamic equilibrium.
10728:
such that the latter is adiabatically accessible from the former but not conversely. Defining the entropies of the reference states to be 0 and 1 respectively, the entropy of a state
10674:
from 1909 and the monograph by R. Giles. In the setting of Lieb and
Yngvason, one starts by picking, for a unit amount of the substance under consideration, two reference states
6944:, he showed that this expression gives a measure of entropy for systems of atoms and molecules in the gas phase, thus providing a measure for the entropy of classical thermodynamics.
9205:
8932:
5686:. Heat transfer in the isotherm steps (isothermal expansion and isothermal compression) of the Carnot cycle was found to be proportional to the temperature of a system (known as its
5470:
16524:
12537:"Ueber verschiedene fĂŒr die Anwendung bequeme Formen der Hauptgleichungen der mechanischen WĂ€rmetheorie (Vorgetragen in der naturforsch. Gesellschaft zu ZĂŒrich den 24. April 1865)"
11120:, when the phases between the basis states are purely random, this expression is equivalent to the familiar classical definition of entropy for states with classical probabilities
8263:
4946:
3745:
3567:
I prefer going to the ancient languages for the names of important scientific quantities, so that they may mean the same thing in all living tongues. I propose, therefore, to call
12137:
10030:
5254:
16388:
10150:
14182:
7010:, the difference in temperature between the warm room (the surroundings) and the cold glass of ice and water (the system and not part of the room) decreases as portions of the
9885:
9789:
7804:
16570:
11719:
The entropy of a substance can be measured, although in an indirect way. The measurement, known as entropymetry, is done on a closed system with constant number of particles
10579:
The concept of entropy can be described qualitatively as a measure of energy dispersal at a specific temperature. Similar terms have been in use from early in the history of
10141:
10591:, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels.
9770:
9670:
6547:
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10545:
10512:
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4074:
4045:
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3271:, and found the link between the microscopic interactions, which fluctuate about an average configuration, to the macroscopically observable behavior, in form of a simple
11041:
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8815:
6518:
4330:{\displaystyle W={\frac {T_{\mathsf {H}}-T_{\mathsf {C}}}{T_{\mathsf {H}}}}\cdot Q_{\mathsf {H}}=\left(1-{\frac {T_{\mathsf {C}}}{T_{\mathsf {H}}}}\right)Q_{\mathsf {H}}}
1224:
1169:
1114:
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11070:
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3702:
921:
874:
789:
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607:
12167:, a full chapter on the economics of Georgescu-Roegen has approvingly been included in one elementary physics textbook on the historical development of thermodynamics.
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6002:
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5981:: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. In any process, where the system gives up
10310:
8178:
continuous operation, an entropy balance applied to an open system accounts for system entropy changes related to heat flow and mass flow across the system boundary.
3839:(i.e., it occurs without any dissipation, deviating only infinitesimally from the thermodynamic equilibrium), and it may conserve total entropy. For example, in the
1059:
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10386:
8115:
8088:
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7834:
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12028:
never decreases in large systems over significant periods of time. Hence, from this perspective, entropy measurement is thought of as a clock in these conditions.
8505:
8485:
8465:
8445:
8383:
7018:
However, as calculated in the example, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. In an
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in 1948 to study the size of information of a transmitted message. The definition of information entropy is expressed in terms of a discrete set of probabilities
7483:
4514:
4488:
4369:
15770:"When, where, and by how much do biophysical limits constrain the economic process? A survey of Nicholas Georgescu-Roegen's contribution to ecological economics"
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1790:
558:
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10602:, which usually have meanings directly opposed to equilibrium, contribute to widespread confusion and hamper comprehension of entropy for most students. As the
897:
850:
765:
718:
630:
583:
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12149:
11978:
11757:
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11709:
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9567:
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8018:
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3645:. State variables depend only on the equilibrium condition, not on the path evolution to that state. State variables can be functions of state, also called
3212:, which states that the entropy of an isolated system left to spontaneous evolution cannot decrease with time. As a result, isolated systems evolve toward
6397:
This definition assumes the basis states to be picked in a way that there is no information on their relative phases. In a general case the expression is:
6341:
5082:{\displaystyle -{\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}-{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}=\Delta S_{\mathsf {r,H}}+\Delta S_{\mathsf {r,C}}=0}
7190:
5862:
3780:
3579:
to be similar to energy, for these two quantities are so analogous in their physical significance, that an analogy of denominations seems to me helpful.
3157:
concept that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from
11903:{\displaystyle T:={\left({\frac {\partial U}{\partial S}}\right)}_{V,N}\ \Rightarrow \ \cdots \ \Rightarrow \ \mathrm {d} S={\frac {\mathrm {d} Q}{T}}}
14209:
9682:
9163:
The nomenclature "entropy balance" is misleading and often deemed inappropriate because entropy is not a conserved quantity. In other words, the term
12391:
The Kind of Motion We Call Heat: a
History of the Kinetic Theory of Gases in the 19th Century, Book 2, Statistical Physics and Irreversible Processes
8696:{\displaystyle {\frac {\mathrm {d} S}{\mathrm {d} t}}=\sum _{k=1}^{K}{{\dot {M}}_{k}{\hat {S}}_{k}+{\frac {\dot {Q}}{T}}+{\dot {S}}_{\mathsf {gen}}}}
7620:
11339:
17993:
16501:
16229:
16169:
15415:
15150:
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11691:
is the
Boltzmann constant, which may be interpreted as the thermodynamic entropy per nat. Some authors argue for dropping the word entropy for the
11259:
11150:
7112:
6215:
5720:
3324:; in any natural process there exists an inherent tendency towards the dissipation of useful energy. In 1824, building on that work, Lazare's son,
1699:
12120:
11522:
7106:
7090:
temperature is at a lower entropy (than if the heat distribution is allowed to even out) and some of the thermal energy can drive a heat engine.
4636:{\displaystyle W-Q_{\Sigma }=W-\left\vert Q_{\mathsf {H}}\right\vert +\left\vert Q_{\mathsf {C}}\right\vert =W-Q_{\mathsf {H}}-Q_{\mathsf {C}}=0}
10234:
As a fundamental aspect of thermodynamics and physics, several different approaches to entropy beyond that of Clausius and Boltzmann are valid.
13766:
12175:
8389:, a quantity that may be either conserved, such as energy, or non-conserved, such as entropy. The basic generic balance expression states that
6610:
1400:
10646:
As the entropy of the universe is steadily increasing, its total energy is becoming less useful. Eventually, this is theorized to lead to the
7042:. Historically, the concept of entropy evolved to explain why some processes (permitted by conservation laws) occur spontaneously while their
12465:
Clausius, Rudolf (1850). "Ăber die bewegende Kraft der WĂ€rme und die Gesetze, welche sich daraus fĂŒr die WĂ€rmelehre selbst ableiten lassen".
10623:, introduces entropy with the statement that "spontaneous changes are always accompanied by a dispersal of energy or matter and often both".
1897:
1288:
6577:. Density matrix formalism is not required if the system occurs to be in a thermal equilibrium so long as the basis states are chosen to be
6163:
12104:
effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.
5932:
We can calculate the change of entropy only by integrating the above formula. To obtain the absolute value of the entropy, we consider the
13397:
7727:â the combination of a subsystem under study and its surroundings â increases during all spontaneous chemical and physical processes. The
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12068:
plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into
522:
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12057:
in which all the energy ends up as a homogeneous distribution of thermal energy so that no more work can be extracted from any source.
11271:
name. In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage.
3502:, a Greek mathematician, linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability.
11297:, the entropy state function is the amount of information in the system that is needed to fully specify the microstate of the system.
9211:
5697:
While Clausius based his definition on a reversible process, there are also irreversible processes that change entropy. Following the
14186:
3137:
1765:
1378:
15288:
Chiavazzo, Eliodoro; Isaia, Marco; Mammola, Stefano; Lepore, Emiliano; Ventola, Luigi; Asinari, Pietro; Pugno, Nicola Maria (2015).
15082:
12181:â a student of Georgescu-Roegen â has been the economics profession's most influential proponent of the entropy pessimism position.
6683:
12514:
Liddell, H. G., Scott, R. (1843/1978). A GreekâEnglish Lexicon, revised and augmented edition, Oxford University Press, Oxford UK,
8023:
5929:
between the same two states. However, the heat transferred to or from the surroundings is different as well as its entropy change.
5544:
and an entropy as shown above prove to be useful in the study of any classical thermodynamic heat engine: other cycles, such as an
5251:
produced by this engine is less than the maximum predicted by Carnot's theorem), its work output is capped by Carnot efficiency as:
2682:
15002:
Kim, Hye Jin; Park, Youngkyu; Kwon, Yoonjin; Shin, Jaeho; Kim, Young-Han; Ahn, Hyun-Seok; Yazami, Rachid; Choi, Jang Wook (2020).
12020:
Entropy is the only quantity in the physical sciences that seems to imply a particular direction of progress, sometimes called an
9575:
7739:
property, meaning that it scales with the size or extent of a system. In many processes it is useful to specify the entropy as an
7530:
7315:
16670:
7529:, so that they have defined entropy. Some inhomogeneous systems out of thermodynamic equilibrium still satisfy the hypothesis of
6902:, then observer A will see a violation of the second law of thermodynamics, since he does not possess information about variable
3330:
1411:
12164:
11992:
Although the concept of entropy was originally a thermodynamic concept, it has been adapted in other fields of study, including
11452:
probable), the Shannon entropy (in bits) is just the number of binary questions needed to determine the content of the message.
17290:
8706:
2212:
7806:
constitute each element's or compound's standard molar entropy, an indicator of the amount of energy stored by a substance at
17617:
17334:
17009:
16542:
16485:
16464:
16445:
16424:
16400:
16373:
16354:
16333:
16310:
16291:
16268:
16246:
16213:
16190:
16153:
16134:
16112:
16089:
16070:
15854:
15824:
15691:
15666:
15641:
15616:
15399:
15233:
15134:
15109:
15066:
14867:
14842:
14812:
14787:
14731:
14612:
14564:
14357:
14302:
14152:
14101:
14076:
13981:
13909:
13621:
13476:
13380:
13353:
13328:
13299:
13274:
13163:
13104:
13079:
13043:
13013:
12988:
12944:
12895:
12870:
12837:
12804:
3466:
gave entropy a statistical basis. In 1877, Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of
981:
5705:
always increases for irreversible processes. The difference between an isolated system and closed system is that energy may
3546:, as he found the concepts nearly "analogous in their physical significance". This term was formed by replacing the root of
17986:
6116:
6098:
5596:
3992:
1739:
1692:
1279:
948:
515:
393:
13125:
7813:
Entropy is equally essential in predicting the extent and direction of complex chemical reactions. For such applications,
7810:. Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture.
4018:
if and only if there is a temperature difference between reservoirs. Originally, Carnot did not distinguish between heats
3510:
In 1865, Clausius named the concept of "the differential of a quantity which depends on the configuration of the system",
17476:
9511:
9266:
For certain simple transformations in systems of constant composition, the entropy changes are given by simple formulas.
8175:
5092:
331:
11762:
7512:
is the temperature of the coldest accessible reservoir or heat sink external to the system. For further discussion, see
18149:
16517:
15567:
14960:
14268:
7740:
7736:
7547:
7374:
7246:
7073:. The molar entropy of ions is obtained as a difference in entropy from a reference state defined as zero entropy. The
7000:
6132:
6128:
5776:
5679:
5588:
2884:
2767:
1734:
1463:
1437:
958:
412:
6980:. It can also be described as the reversible heat divided by temperature. Entropy is a fundamental function of state.
4670:
14931:
12638:
12398:
7704:
6335:
6086:
364:
8362:
To derive a generalized entropy balanced equation, we start with the general balance equation for the change in any
7366:
It follows from the second law of thermodynamics that the entropy of a system that is not isolated may decrease. An
7272:
6585:. For most practical purposes it can be taken as the fundamental definition of entropy since all other formulae for
17417:
16510:
Entropy and the Tao of Counting: A Brief Introduction to Statistical Mechanics and the Second Law of Thermodynamics
16033:
14628:
Lieb, Elliott H.; Yngvason, Jakob (March 1999). "The physics and mathematics of the second law of thermodynamics".
8392:
8154:
in 2007. The world's effective capacity to exchange information through two-way telecommunication networks was 281
7262:
7046:(also permitted by conservation laws) do not; systems tend to progress in the direction of increasing entropy. For
3342:
can be produced from the actions of its fall from a hot to cold body. He used an analogy with how water falls in a
1516:
987:
386:
15290:"Cave spiders choose optimal environmental factors with respect to the generated entropy when laying their cocoon"
9522:
For pure heating or cooling of any system (gas, liquid or solid) at constant pressure from an initial temperature
7326:
The probability density function is proportional to some function of the ensemble parameters and random variables.
18283:
17979:
12936:
The Mechanical Theory of Heat: With Its Applications to the Steam-engine and to the Physical Properties of Bodies
10485:
is the "disorder" capacity of the system, which is the entropy of the parts contained in the permitted ensemble,
8997:
6968:
6582:
1685:
14949:"Use of Receding Horizon Optimal Control to Solve MaxEP-Based (max entropy production) Biogeochemistry Problems"
11633:
8297:
across the system boundaries cause changes in the entropy of the system. Heat transfer entails entropy transfer
6726:
In thermodynamics, such a system is one with a fixed volume, number of molecules, and internal energy, called a
3216:, where the entropy is highest. A consequence of the second law of thermodynamics is that certain processes are
18341:
17885:
17427:
15882:
15774:
15707:
12519:
12367:
11668:
3051:
2430:
1616:
148:
14723:
Mathematical Foundations of Thermodynamics: International Series of Monographs on Pure and Applied Mathematics
8146:
in 2007. The world's technological capacity to receive information through one-way broadcast networks was 432
3325:
1511:
18490:
18245:
15930:
13637:
Saha, Arnab; Lahiri, Sourabh; Jayannavar, A. M. (2009). "Entropy production theorems and some consequences".
10909:
6159:
5576:
3483:
3475:
3284:
3276:
3130:
2922:
2918:
2826:
1758:
1591:
1364:
341:
13925:
Jungermann, A.H. (2006). "Entropy and the Shelf Model: A Quantum Physical Approach to a Physical Property".
9166:
8893:
6733:
The most general interpretation of entropy is as a measure of the extent of uncertainty about a system. The
5435:
18470:
17654:
17597:
16957:
13698:
Martyushev, L. M.; Seleznev, V. D. (2014). "The restrictions of the maximum entropy production principle".
12262:
11298:
11255:
10603:
10277:
8187:
8126:
7966:{\displaystyle \Delta S_{\mathsf {universe}}=\Delta S_{\mathsf {surroundings}}+\Delta S_{\mathsf {system}}}
7720:
7343:
7074:
7065:
Unlike many other functions of state, entropy cannot be directly observed but must be calculated. Absolute
5698:
5557:
3347:
3209:
2675:
976:
179:
169:
15345:
Thanos, Dimitrios; Li, Wentian; Provata, Astero (1 March 2018). "Entropic fluctuations in DNA sequences".
12766:
8230:
6085:
is not required: for example, the entropy of a mixture of two moles of hydrogen and one mole of oxygen in
5425:{\displaystyle {\frac {Q_{\mathsf {H}}}{T_{\mathsf {H}}}}+{\frac {Q_{\mathsf {C}}}{T_{\mathsf {C}}}}<0}
4909:
4080:
to be valid and hence that the total heat in the system was conserved. But in fact, the magnitude of heat
3712:
18091:
17516:
16775:
16663:
15165:
12716:
12040:
proposed that where cave spiders choose to lay their eggs can be explained through entropy minimization.
10612:
7050:, entropy never decreases. This fact has several important consequences in science: first, it prohibits "
5933:
4717:
3666:, the working fluid returns to the same state that it had at the start of the cycle, hence the change or
3586:
added that in this way "he succeeded in coining a word that meant the same thing to everybody: nothing".
3362:
2771:
184:
174:
15973:
14216:
11759:, and it uses the definition of temperature in terms of entropy, while limiting energy exchange to heat
7086:, plays an important role in determining in which direction a chemical reaction spontaneously proceeds.
18336:
18061:
17762:
17678:
16325:
13320:
12618:
12160:
12141:
12124:
12054:
11007:{\displaystyle S=-k_{\mathsf {B}}\ \mathrm {tr} {\left({\hat {\rho }}\times \ln {\hat {\rho }}\right)}}
10647:
10584:
10556:
6484:{\displaystyle S=-k_{\mathsf {B}}\ \mathrm {tr} {\left({\hat {\rho }}\times \ln {\hat {\rho }}\right)}}
3487:
2747:
1468:
1432:
210:
144:
13226:
Jaynes, E. T. (1992). "The Gibbs Paradox". In Smith, C. R.; Erickson, G. J.; Neudorfer, P. O. (eds.).
10671:
6963:
4437:{\textstyle Q_{\Sigma }=\left\vert Q_{\mathsf {H}}\right\vert -\left\vert Q_{\mathsf {C}}\right\vert }
3499:
1506:
18119:
17422:
17280:
16942:
16887:
16867:
16862:
12133:
10117:
8355:
7766:
7526:
6078:
5675:
3638:
3213:
2859:
1261:
1009:
455:
268:
258:
15922:
12862:
5629:
18480:
18255:
18197:
18124:
18056:
17938:
17921:
17351:
16695:
16629:
15870:
11113:
10580:
7258:
6615:
6527:
5970:
3634:
3614:
3320:
proposed that in any machine, the accelerations and shocks of the moving parts represent losses of
3264:
3158:
3123:
3110:
3000:
2864:
2834:
2780:
2495:
2217:
1969:
1751:
21:
15058:
13155:
13071:
10253:
a measure of disorder in the universe or of the availability of the energy in a system to do work.
9746:
9646:
7525:
The applicability of a second law of thermodynamics is limited to systems in or sufficiently near
7359:
machine. It follows that a reduction in the increase of entropy in a specified process, such as a
18260:
18215:
18154:
18086:
18046:
17785:
17775:
17701:
17573:
17511:
17496:
16892:
16872:
15250:
14951:. In Dewar, Roderick C.; Lineweaver, Charles H.; Niven, Robert K.; Regenauer-Lieb, Klaus (eds.).
14458:
12272:
11475:
is the number of microstates that can yield a given macrostate, and each microstate has the same
11079:
10659:
10521:
10488:
10459:
10144:
9997:
7716:
7250:
7055:
6727:
6621:
6293:
6050:
5917:
Therefore thermodynamic entropy has the dimension of energy divided by temperature, and the unit
5614:
4169:
4112:
4083:
4050:
4021:
3961:
3932:
3899:
3870:
2888:
2839:
2802:
2739:
2668:
2651:
2272:
2187:
1724:
1673:
1501:
1298:
1179:
1124:
1069:
1001:
940:
476:
465:
131:
28:
12630:
11017:
9060:
8820:
8784:
6494:
3613:
The concept of entropy is described by two principal approaches, the macroscopic perspective of
1965:
903:
856:
771:
724:
636:
589:
18346:
18187:
17832:
17024:
16920:
16847:
16837:
16718:
16656:
13401:
13266:
12829:
12221:
12206:
12156:
11938:
11913:
11239:
11235:
11050:
8120:
7266:
7066:
6209:
5207:
5183:
3682:
3650:
3555:
3370:
3101:
2505:
2485:
2355:
1606:
1323:
407:
161:
136:
15555:
14948:
14947:
Vallino, Joseph J.; Algar, Christopher K.; GonzĂĄlez, Nuria FernĂĄndez; Huber, Julie A. (2013).
14507:
14256:
11228:
Von Neumann established a rigorous mathematical framework for quantum mechanics with his work
10838:
8960:
8856:
8300:
5984:
3373:
in all processes; the first law, however, is unsuitable to separately quantify the effects of
1526:
807:
672:
18182:
18159:
18076:
17717:
17640:
16964:
16755:
14554:
12201:
12108:
10261:
10242:
The following is a list of additional definitions of entropy from a collection of textbooks:
10103:{\displaystyle \Delta S_{\mathsf {fus}}={\frac {\Delta H_{\mathsf {fus}}}{T_{\mathsf {m}}}}.}
8268:
8191:
7378:
7311:
5564:
5323:{\displaystyle W<\left(1-{\frac {T_{\mathsf {C}}}{T_{\mathsf {H}}}}\right)Q_{\mathsf {H}}}
4723:
Finally, comparison for the both representations of a work output in a Carnot cycle gives us:
3618:
3268:
3096:
3029:
3024:
2892:
2150:
1541:
1118:
431:
277:
126:
15050:
14318:
13258:
13147:
13063:
12854:
12411:
10220:{\displaystyle \Delta S_{\mathsf {vap}}={\frac {\Delta H_{\mathsf {vap}}}{T_{\mathsf {b}}}}}
8201:
7427:
1029:
18318:
18278:
18220:
17860:
17412:
17385:
17363:
17270:
17203:
16952:
16882:
16827:
16583:
15943:
15740:
15512:
15493:(April 1996). "Surface tension, hydrophobicity, and black holes: The entropic connection".
15448:
15354:
15301:
15262:
15180:
14647:
14519:
14431:
14385:
14125:
14013:
13934:
13849:
13793:
13717:
13656:
13576:
13511:
13439:
13192:
12855:
12548:
12474:
12325:
12145:
12005:
11263:
10295:
8386:
8183:
7024:
6984:
6957:
6124:
6082:
5978:
5702:
5687:
4339:
3459:
3400:
3217:
2282:
2160:
2145:
2135:
1887:{\displaystyle {\hat {H}}|\psi _{n}(t)\rangle =i\hbar {\frac {d}{dt}}|\psi _{n}(t)\rangle }
1621:
1546:
1536:
336:
198:
10791:
10751:
8097:
8070:
7980:
7836:
must be incorporated in an expression that includes both the system and its surroundings:
7816:
7404:
6556:
6027:
3867:
performed by a Carnot heat engine as a reversible heat engine. In a Carnot cycle the heat
2390:
2009:
8:
18298:
18192:
18134:
18031:
17926:
17905:
17491:
17434:
17356:
17329:
17014:
16877:
16852:
15874:
15765:
15711:
15051:
14233:
13838:"Self-assembled wiggling nano-structures and the principle of maximum entropy production"
13148:
13064:
10917:
10903:
9971:{\displaystyle \Delta S=nC_{\mathrm {P} }\ln {\frac {T}{T_{0}}}-nR\ln {\frac {P}{P_{0}}}}
9875:{\displaystyle \Delta S=nC_{\mathrm {V} }\ln {\frac {T}{T_{0}}}+nR\ln {\frac {V}{V_{0}}}}
8490:
8470:
8450:
8430:
8368:
6930:
6662:
6171:
6147:
5563:
For further analysis of sufficiently discrete systems, such as an assembly of particles,
3864:
3836:
3463:
3412:
3190:
3162:
3105:
3080:
3063:
2972:
2872:
2806:
2729:
2405:
2232:
2222:
2170:
2165:
2140:
2039:
1566:
1328:
350:
316:
311:
224:
15947:
15744:
15516:
15452:
15358:
15305:
15266:
15184:
14651:
14523:
14435:
14389:
14129:
14017:
13938:
13853:
13797:
13721:
13660:
13580:
13515:
13443:
13196:
12552:
12478:
12329:
9514:, where the temperature, internal energy and enthalpy for an ideal gas remain constant.
7458:
6162:(or kgâ
mâ
sâ
K in terms of base units). The entropy of a substance is usually given as an
4493:
4467:
4348:
4342:
in a letter to Kelvin. This allowed Kelvin to establish his absolute temperature scale.
2490:
1561:
540:
18485:
18444:
18439:
18394:
18351:
18313:
18270:
18129:
17953:
17865:
17842:
17823:
17803:
17767:
17471:
17449:
17439:
17275:
16532:
16495:
16414:
16280:
16223:
16163:
16001:
15989:
15903:
15730:
15536:
15502:
15490:
15472:
15438:
15409:
15322:
15289:
15196:
15144:
15031:
14920:
14900:
14760:
14702:
14663:
14637:
14535:
14401:
14162:
14047:
13970:
13950:
13898:
13870:
13837:
13760:
13733:
13707:
13680:
13646:
13594:
13566:
13535:
13501:
12822:
12668:
12648:
12623:
12442:
12435:
Treatise on the Mechanical Theory of Heat and its Applications to the Steam-Engine, etc
12356:
12351:
12211:
12171:
12073:
12044:
evolutionary trees by determining the evolutionary distance between different species.
11993:
11711:
function of information theory and using Shannon's other term, "uncertainty", instead.
11484:
11477:
11312:
11294:
11123:
11106:
10870:
10811:
10704:
10677:
10303:
9783:
9525:
9507:
9308:
9281:
9116:
8935:
8363:
7488:
7254:
6320:
6184:
6140:
6109:
5649:
5622:
5231:
If we consider a heat engine which is less effective than Carnot cycle (i.e., the work
3988:
3926:
3479:
3307:
3280:
3202:
3198:
3166:
3075:
2996:
2992:
2934:
2926:
2797:
2615:
2565:
2515:
2257:
2252:
2192:
2057:
1729:
1655:
1318:
1313:
1266:
882:
835:
750:
703:
615:
568:
498:
482:
369:
321:
306:
296:
105:
99:
15792:
15769:
15274:
14659:
7265:. These proofs are based on the probability density of microstates of the generalized
2305:
18356:
18328:
18051:
18021:
17958:
17855:
17828:
17739:
17729:
17722:
17696:
17580:
17373:
17198:
17059:
17019:
16989:
16974:
16947:
16857:
16760:
16700:
16690:
16538:
16513:
16481:
16475:
16460:
16441:
16435:
16420:
16396:
16369:
16350:
16329:
16306:
16287:
16264:
16242:
16209:
16186:
16149:
16130:
16108:
16085:
16066:
15993:
15907:
15850:
15820:
15687:
15662:
15637:
15612:
15606:
15563:
15528:
15464:
15395:
15389:
15370:
15327:
15229:
15130:
15105:
15062:
15035:
15023:
14956:
14927:
14904:
14863:
14838:
14808:
14783:
14727:
14706:
14667:
14608:
14560:
14488:
14473:
14443:
14405:
14353:
14298:
14292:
14264:
14148:
14097:
14072:
14051:
14039:
14031:
13977:
13905:
13875:
13737:
13672:
13617:
13598:
13539:
13527:
13472:
13376:
13349:
13324:
13295:
13270:
13259:
13208:
13159:
13100:
13075:
13039:
13009:
12984:
12940:
12891:
12866:
12833:
12800:
12741:
12634:
12515:
12394:
12363:
12313:
12191:
12129:
12101:
12090:
12024:. As time progresses, the second law of thermodynamics states that the entropy of an
10588:
10024:
8939:
8133:
7974:
7700:
7573:
to changes in the entropy and the external parameters. This relation is known as the
7360:
7352:
7348:
7329:
Thermodynamic state functions are described by ensemble averages of random variables.
7094:
6988:
6734:
6178:
5943:
5691:
4883:
Similarly to the derivation of internal energy, this equality implies existence of a
3471:
2908:
2868:
2759:
2743:
2712:
2575:
2435:
2345:
2340:
2155:
2029:
2004:
1650:
1611:
1601:
1173:
971:
799:
301:
291:
233:
16005:
15200:
14539:
13954:
13684:
8138:
technological capacity to store information grew from 2.6 (entropically compressed)
7269:
and the identification of the thermodynamic internal energy as the ensemble average
3575:
of a body, after the Greek word "transformation". I have designedly coined the word
2500:
18465:
18366:
18144:
18071:
17850:
17532:
17506:
17501:
17481:
17466:
17307:
17297:
17077:
17004:
16740:
16101:
15985:
15951:
15899:
15895:
15787:
15540:
15520:
15476:
15456:
15362:
15317:
15309:
15270:
15221:
15188:
15015:
14892:
14694:
14655:
14527:
14439:
14393:
14021:
14002:"The World's Technological Capacity to Store, Communicate, and Compute Information"
13942:
13865:
13857:
13801:
13725:
13664:
13584:
13519:
13447:
13200:
13180:
12556:
12490:
12482:
12386:
12373:
12333:
12267:
12241:
12226:
12196:
12097:
12096:
The role of entropy in cosmology remains a controversial subject since the time of
12081:
11963:
11742:
11722:
11694:
11674:
11613:
11458:
11441:
11301:
is the measure of the amount of missing information before reception. Often called
11281:
10913:
10771:
10731:
10515:
10247:
9986:
9673:
9552:
9489:
9465:
9355:
9335:
9143:
9096:
8943:
8890:
is the rate of entropy flow due to the flow of heat across the system boundary and
8531:
8511:
8337:
8003:
7728:
7679:
7600:
7580:
7556:
7384:
7356:
7051:
7007:
6934:
6905:
6885:
6865:
6845:
6825:
6805:
6785:
6765:
6745:
6588:
6574:
6326:
In case states are defined in a continuous manner, the summation is replaced by an
6104:
6007:
5838:
5714:
5333:
5234:
5163:
4889:
4650:
4447:
4149:
4001:
3755:
3455:
3408:
3259:
3041:
3016:
2984:
2942:
2880:
2755:
2630:
2605:
2580:
2570:
2525:
2395:
2202:
2182:
2177:
2034:
1571:
1556:
1496:
1491:
1308:
1303:
953:
421:
286:
17900:
16642:
15955:
13424:
12060:
If the universe can be considered to have generally increasing entropy, then â as
10670:
in 1999. This approach has several predecessors, including the pioneering work of
10634:
It is possible (in a thermal context) to regard lower entropy as a measure of the
8158:
of (entropically compressed) information in 1986, to 65 (entropically compressed)
8000:
for reactants and products in the system at the constant pressure and temperature
3958:
is transferred from a working gas to a cold reservoir at the constant temperature
18414:
18361:
18250:
18207:
18139:
18096:
18081:
18041:
17895:
17890:
17818:
17813:
17780:
17707:
17561:
17542:
17456:
17223:
17138:
16994:
16984:
16969:
16927:
16832:
16782:
16733:
16617:
16319:
15843:
The Second Law of Life: Energy, Technology, and the Future of Earth As We Know It
15841:
15215:
14721:
14066:
13129:
12934:
12085:
12025:
12001:
11117:
10663:
10607:
7724:
7367:
7078:
7069:
of a substance can be calculated from the measured temperature dependence of its
7047:
7019:
5671:
5667:
5654:
4948:
and which is conserved over an entire cycle. Clausius called this state function
4713:
4139:
3896:
is transferred from a hot reservoir to a working gas at the constant temperature
3856:
3705:
of a system excluding its surroundings can be well-defined as a small portion of
3563:
In more detail, Clausius explained his choice of "entropy" as a name as follows:
3522:) after the Greek word for 'transformation'. He gave "transformational content" (
3385:
3299:
3236:
3224:
3012:
3008:
2938:
2876:
2830:
2792:
2775:
2763:
2734:
2625:
2620:
2540:
2480:
2385:
2360:
2350:
2315:
2310:
2277:
2207:
2130:
1989:
1521:
1369:
1023:
664:
487:
248:
215:
16179:
15366:
15192:
14832:
13729:
13372:
The Macroscope â a New World View (written by an M.I.T.-trained biochemist)
10514:
is the "information" capacity of the system, an expression similar to Shannon's
7719:, enabling changes to be quantified and the outcome of reactions predicted. The
18404:
18381:
18308:
18066:
18002:
17943:
17659:
17537:
17486:
17461:
17265:
17230:
17163:
17153:
17069:
17049:
17044:
17029:
16999:
16979:
16937:
16915:
16897:
16797:
16787:
16723:
16579:â an A-level physics lecture with 'derivation' of entropy based on Carnot cycle
16122:
15718:
15460:
14600:
14556:
Atkins' Physical Chemistry 11e: Volume 3: Molecular Thermodynamics and Kinetics
13668:
13589:
13554:
13122:
12495:
12216:
11997:
11306:
11277:
11243:
11044:
10667:
10376:{\displaystyle {\mathsf {Disorder}}={\frac {C_{\mathsf {D}}}{C_{\mathsf {I}}}}}
10299:
10257:
7031:
7011:
6926:
6521:
6331:
5974:
5832:
4884:
4645:
4077:
3996:
3659:
3646:
3642:
3339:
3335:
3194:
3071:
3004:
2958:
2751:
2698:
2610:
2595:
2555:
2545:
2520:
2465:
2415:
2410:
2247:
2227:
2197:
2082:
2019:
2014:
1781:
1576:
1346:
446:
326:
263:
253:
121:
91:
16636:
16608:
16603:
16598:
16593:
16588:
16576:
16559:
15225:
14896:
12337:
12121:
Nicholas Georgescu-Roegen § The relevance of thermodynamics to economics
12107:
Current theories suggest the entropy gap to have been originally opened up by
11234:. He provided in this work a theory of measurement, where the usual notion of
10449:{\displaystyle {\mathsf {Order}}=1-{\frac {C_{\mathsf {O}}}{C_{\mathsf {I}}}}}
7676:
Since both internal energy and entropy are monotonic functions of temperature
4338:
the temperature as measured from a zero point of temperature was suggested by
3338:" (what is now known as heat) falls through a temperature difference, work or
18459:
18409:
18371:
18230:
17931:
17585:
17444:
17404:
17368:
17324:
17250:
17213:
17131:
17054:
16822:
16817:
16770:
16750:
16410:
16058:
15524:
15374:
15027:
14778:
Balian, Roger (2004). "Entropy, a Protean concept". In Dalibard, Jean (ed.).
14492:
14035:
13227:
13212:
13136:; Beisbart C. and Hartmann, S. (eds.); Oxford University Press, Oxford, 2010.
12560:
12486:
12077:
12061:
12021:
9640:
7070:
7059:
6578:
5937:
5553:
3774:
3667:
3655:
3602:
3351:
3317:
3223:
The thermodynamic concept was referred to by Scottish scientist and engineer
3161:, where it was first recognized, to the microscopic description of nature in
2947:
2814:
2585:
2550:
2510:
2475:
2455:
2450:
2445:
2440:
2420:
2365:
2300:
1645:
963:
532:
493:
205:
16202:
14026:
14001:
10643:
overall increase in entropy represents a "loss" that can never be replaced.
8121:
World's technological capacity to store and communicate entropic information
6323:
and the summation is performed over all possible microstates of the system.
5666:
The thermodynamic definition of entropy was developed in the early 1850s by
3670:
of any state function, such as entropy, over this reversible cycle is zero.
2460:
18303:
18235:
18164:
17948:
17341:
17285:
17235:
17218:
17039:
16812:
16745:
16564:
16383:
16256:
15997:
15468:
15331:
14043:
13879:
13806:
13781:
13676:
13531:
12246:
12236:
12231:
10788:
is adiabatically accessible from a composite state consisting of an amount
10616:
10291:
10111:
9776:
9455:{\displaystyle \Delta S=nR\ln {\frac {V}{V_{0}}}=-nR\ln {\frac {P}{P_{0}}}}
9258:
with zero for reversible process and positive values for irreversible one.
6977:
5683:
5567:
must be used. Additionally, description of devices operating near limit of
5549:
5541:
3860:
3840:
3663:
3416:
3404:
3355:
3067:
2897:
2818:
2600:
2425:
2400:
2375:
2330:
2325:
2262:
2242:
1596:
1581:
1531:
1014:
75:
15532:
15004:"Entropymetry for non-destructive structural analysis of LiCoO 2 cathodes"
12292:
The overdots represent derivatives of the quantities with respect to time.
6972:
and faint-blue is steam. Grey-blue represents supercritical liquid water.)
3512:
18434:
18429:
18419:
18389:
18288:
18240:
18174:
17757:
17752:
17346:
17312:
17186:
17176:
17119:
17102:
17087:
17034:
16932:
16625:
16320:
Haddad, Wassim M.; Chellaboina, VijaySekhar; Nersesov, Sergey G. (2005).
15969:
15807:
15735:
15722:
15507:
14860:
The Physical Foundation of Economics â an Analytical Thermodynamic Theory
14642:
14474:"Undergraduate students' understandings of entropy and Gibbs free energy"
12257:
12178:
11285:
11073:
9483:
7745:
7105:
Proofs of equivalence between the entropy in statistical mechanics â the
6996:
6992:
6550:
5682:
thermodynamic variable that was shown to be useful in characterizing the
5637:
5568:
4143:
3749:
3583:
3378:
3366:
3343:
3283:, that has become one of the defining universal constants for the modern
3091:
3055:
3046:
3020:
2988:
2967:
2962:
2930:
2822:
2590:
2560:
2530:
2335:
2092:
1551:
359:
27:
For a more accessible and less technical introduction to this topic, see
17609:
16573:
MIT OCW lecture, part of 5.60 Thermodynamics & Kinetics, Spring 2008
15632:
Lineweaver, Charles H.; Davies, Paul C. W.; Ruse, Michael, eds. (2013).
14764:
14748:
8170:
6987:, pressure and temperature tend to become uniform over time because the
6181:
measure for the system with a number of states, each with a probability
18225:
18111:
17747:
17380:
17302:
17240:
17208:
17148:
16842:
15556:"A Look at the Concept of Channel Capacity from a Maxwellian Viewpoint"
15443:
15217:
The Unity of Science and Economics: A New Foundation of Economic Theory
15019:
15003:
14953:
Beyond the Second Law: Entropy Production & Non-equilibrium Systems
14698:
14397:
13946:
12251:
12069:
11516:
11440:
where the base of the logarithm determines the units (for example, the
10287:
8487:
leaves the system across the system boundaries, plus the rate at which
8151:
7332:
At infinite temperature, all the microstates have the same probability.
7043:
6136:
5572:
5545:
2854:
2810:
2470:
2380:
2320:
2237:
2087:
2024:
1994:
1984:
1957:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}
1640:
1586:
15313:
15166:"Inference of analytical thermodynamic models for biological networks"
14552:
14531:
14422:
Landsberg, P.T. (1984). "Can Entropy and "Order" Increase Together?".
13861:
13523:
13294:(Rev. ed.). Sausalito, Calif.: Univ. Science Books. p. 817.
13204:
13066:
Statistical mechanics : entropy, order parameters, and complexity
11246:
he extended the classical concept of entropy into the quantum domain.
11238:
is described as an irreversible process (the so-called von Neumann or
10283:
9269:
5533:{\displaystyle \Delta S_{\mathsf {r,H}}+\Delta S_{\mathsf {r,C}}>0}
18293:
18106:
18016:
17808:
17390:
17317:
17191:
17171:
17143:
17082:
14376:
Landsberg, P.T. (1984). "Is Equilibrium always an Entropy Maximum?".
13452:
12569:
einen bezeichnenden Namen, so könnte man, Àhnlich wie von der Gröƿse
12009:
10611:
even though the total energy remains constant in accordance with the
9510:. These equations also apply for expansion into a finite vacuum or a
9275:
8951:
8155:
7310:. Thermodynamic relations are then employed to derive the well-known
7039:
4195:
absorbed by a working body of the engine during isothermal expansion:
3467:
3272:
3186:
3182:
3178:
3170:
3059:
2850:
2717:
2535:
2267:
238:
14682:
12625:
The Edge of Objectivity: An Essay in the History of Scientific Ideas
12536:
9882:
Similarly if the temperature and pressure of an ideal gas both vary:
6618:) each microstate is assumed to be populated with equal probability
6390:{\displaystyle S=-k_{\mathsf {B}}\left\langle \ln {p}\right\rangle }
3482:, has become one of the defining universal constants for the modern
18399:
17712:
17126:
17107:
17092:
16792:
15939:
15891:
15783:
13571:
13506:
8947:
8159:
8147:
8143:
8139:
8091:
7238:{\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}}
7083:
6327:
5910:{\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}}
5609:
3828:{\displaystyle \mathrm {d} S={\frac {\delta Q_{\mathsf {rev}}}{T}}}
3748:
transferred to the system during reversible process divided by the
3490:
has been to determine the distribution of a given amount of energy
3374:
2980:
2370:
2107:
1999:
1354:
1271:
1063:
471:
243:
35:
17971:
13712:
13651:
6952:
3415:. That was in contrast to earlier views, based on the theories of
17260:
16416:
The Road to Reality: A Complete Guide to the Laws of the Universe
14581:
12065:
10383:
Similarly, the total amount of "order" in the system is given by:
9991:
7035:
4444:
absorbed over a cycle. Thus, with the sign convention for a heat
3622:
3174:
3154:
2913:
64:
16645:â Yale OYC lecture, part of Fundamentals of Physics I (PHYS 200)
14922:
Entropy demystified the second law reduced to plain common sense
14508:"Disorder â A Cracked Crutch for Supporting Entropy Discussions"
13469:
Thermodynamics and an Introduction to Thermostatistics (2nd ed.)
9736:{\displaystyle \Delta S=nC_{\mathrm {V} }\ln {\frac {T}{T_{0}}}}
16807:
16728:
16679:
14883:
Kalinin, M.I.; Kononogov, S.A. (2005). "Boltzmann's constant".
13895:
13370:
9372:
at any constant temperature, the change in entropy is given by:
9261:
7669:{\displaystyle \mathrm {d} U=T\ \mathrm {d} S-p\ \mathrm {d} V}
7514:
6155:
5922:
3528:) as a synonym, paralleling his "thermal and ergonal content" (
2077:
2072:
14350:
Evolution as entropy : toward a unified theory of biology
14122:
Thermodynamics of Complex Systems: Principles and applications
13123:
Frigg, R. and Werndl, C. "Entropy â A Guide for the Perplexed"
11433:{\displaystyle H(X)=-\sum _{i=1}^{n}{p(x_{i})\log {p(x_{i})}}}
9779:, so the assumption of constant heat capacity does not apply.
6330:
over all possible states, or equivalently we can consider the
3470:
particles, in which he defined entropy as proportional to the
15164:
Chiavazzo, Eliodoro; Fasano, Matteo; Asinari, Pietro (2013).
12170:
In economics, Georgescu-Roegen's work has generated the term
11218:{\displaystyle S=-k_{\mathsf {B}}\sum _{i}{p_{i}\ln {p_{i}}}}
9629:{\textstyle \Delta S=nC_{\mathrm {P} }\ln {\frac {T}{T_{0}}}}
8467:
enters the system at the boundaries, minus the rate at which
7973:
Via additional steps this expression becomes the equation of
7180:{\displaystyle S=-k_{\mathsf {B}}\sum _{i}{p_{i}\ln {p_{i}}}}
6283:{\displaystyle S=-k_{\mathsf {B}}\sum _{i}{p_{i}\ln {p_{i}}}}
6151:
5918:
5766:{\displaystyle \oint {\frac {\delta Q_{\mathsf {rev}}}{T}}=0}
5089:
Here we denote the entropy change for a thermal reservoir by
3553:
3547:
2102:
2062:
14064:
13823:
Non-equilibrium Thermodynamics and the Production of Entropy
11603:{\displaystyle H=-\sum _{i=1}^{W}{p_{i}\ln {p_{i}}}=\ln {W}}
8186:, the principles of thermodynamics are commonly applied to "
8165:
17181:
17114:
17097:
16765:
16615:
16346:
Anxiety and the Equation: Understanding Boltzmann's Entropy
15287:
14780:
PoincarĂ© Seminar 2003: Bose-Einstein condensation â entropy
14294:
Q is for quantum : an encyclopedia of particle physics
8198:
flow across the system boundary. In general, flow of heat
8195:
6167:
5670:
and essentially describes how to measure the entropy of an
3706:
3358:, "no change occurs in the condition of the working body".
3295:
2112:
2067:
436:
16604:
Reconciling Thermodynamic and State Definitions of Entropy
15847:(Link to the author's science blog, based on his textbook)
15560:
Physics of Multiantenna Systems & Broadband Processing
12590:
nach dem griechischen Worte áŒĄ ÏÏÎżÏÎź, die Verwandlung, die
10658:
A definition of entropy based entirely on the relation of
10260:
per unit temperature that is unavailable for doing useful
8774:{\textstyle \sum _{k=1}^{K}{{\dot {M}}_{k}{\hat {S}}_{k}}}
3995:, a heat engine with two thermal reservoirs can produce a
3474:
of the number of microstates such a gas could occupy. The
3451:. The word was adopted into the English language in 1868.
16648:
15554:
Sarkar, T.K.; Salazar-Palma, M.; Mokole, Eric L. (2008).
15553:
15057:( ed.). San Francisco, CA : Addison Wesley. p.
14977:
14946:
13425:"On the So-Called Gibbs Paradox, and on the Real Paradox"
13265:(4th ed.). New York: John Wiley & Sons. p.
11445:
8781:
is the net rate of entropy flow due to the flows of mass
8150:
of (entropically compressed) information in 1986, to 1.9
7541:
7027:
is a measure of how far the equalization has progressed.
3637:
are defined by physical variables that define a state of
3628:
16277:
14826:
14824:
12721:. Vol. 1. Longmans, Green, and Co. 1906. p. 11
12718:
The scientific papers of J. Willard Gibbs in Two Volumes
12076:
is proportional to the surface area of the black hole's
10626:
6139:) of the system. The constant of proportionality is the
5678:
with its parts. Clausius created the term entropy as an
4371:
produced by an engine over a cycle equals to a net heat
16530:
16300:
15592:
Cosmogenesis : The Growth of Order in the Universe
14352:(2nd ed.). Chicago : University of Chicago Press.
12703:
An Introduction to the Meaning and Structure of Physics
11960:
is introduced into the system at a certain temperature
10615:(compare discussion in next section). Physical chemist
10282:
Entropy is often loosely associated with the amount of
9777:
heat capacities of solids quickly drop off to near zero
3447:, in 1865 Clausius coined the name of that property as
3177:, in biological systems and their relation to life, in
16146:
Thermodynamics and an Introduction to Thermostatistics
16026:"Entropia â fyzikĂĄlna veliÄina vesmĂru a nĂĄĆĄho ĆŸivota"
15163:
14955:. Living Systems as Catalysts. Springer. p. 340.
14683:"Untersuchungen ĂŒber die Grundlagen der Thermodynamik"
14605:
Energy and Empire: A Biographical Study of Lord Kelvin
14261:
Energy & Entropy: Equilibrium to Stationary States
13070:( ed.). Oxford: Oxford University Press. p.
11966:
11941:
11916:
11765:
11745:
11725:
11697:
11677:
11616:
11487:
11461:
11315:
11126:
11082:
11053:
11020:
10873:
10841:
10814:
10794:
10774:
10754:
10734:
10707:
10680:
10653:
10524:
10491:
10462:
10229:
10000:
9749:
9649:
9578:
9555:
9528:
9492:
9468:
9358:
9338:
9311:
9284:
9169:
9146:
9119:
9099:
9063:
9000:
8963:
8896:
8859:
8823:
8817:
into and out of the system with entropy per unit mass
8787:
8709:
8534:
8514:
8493:
8473:
8453:
8433:
8395:
8371:
8340:
8303:
8271:
8233:
8204:
8100:
8073:
8006:
7983:
7819:
7769:
7682:
7603:
7583:
7559:
7491:
7461:
7430:
7407:
7387:
7275:
6908:
6888:
6868:
6848:
6828:
6808:
6788:
6768:
6748:
6665:
6624:
6591:
6497:
6296:
6187:
6150:
of energy divided by temperature, which has a unit of
6053:
6030:
6010:
5946:
5841:
5779:
5438:
5336:
5237:
5210:
5186:
5166:
5095:
4912:
4892:
4673:
4653:
4496:
4470:
4450:
4377:
4351:
4172:
4152:
4115:
4086:
4053:
4024:
4004:
3964:
3935:
3902:
3873:
3758:
3715:
3685:
16534:
Maxwell's Demon: Why Warmth Disperses and Time Passes
16363:
15347:
Physica A: Statistical Mechanics and Its Applications
15173:
Physica A: Statistical Mechanics and Its Applications
15127:
Information Theory, Evolution, and the Origin of Life
14821:
14263:. Springer Science+Business Media. pp. 138â140.
14000:
Hilbert, Martin; LĂłpez, Priscila (11 February 2011).
13700:
Physica A: Statistical Mechanics and Its Applications
13491:
13261:
Chemical, biochemical, and engineering thermodynamics
12671:
12651:
12358:
The Tragicomical History of Thermodynamics, 1822â1854
12015:
11910:
The resulting relation describes how entropy changes
11801:
11636:
11525:
11342:
11225:
i.e. in such a basis the density matrix is diagonal.
11153:
10926:
10389:
10313:
10153:
10120:
10033:
9888:
9792:
9685:
9378:
9214:
8554:
8026:
7842:
7710:
7623:
7373:
In mechanics, the second law in conjunction with the
7193:
7115:
6686:
6614:, among system microstates of the same energy (i.e.,
6559:
6530:
6403:
6344:
6218:
5987:
5865:
5723:
5478:
5356:
5257:
4962:
4729:
4522:
4201:
3783:
1900:
1793:
1182:
1127:
1072:
1032:
906:
885:
859:
838:
810:
774:
753:
727:
706:
675:
639:
618:
592:
571:
543:
16454:
16079:
15727:
Science and Ultimate Reality: From Quantum to Cosmos
15631:
14459:"A Student's Approach to the Second Law and Entropy"
13636:
12978:
12857:
The tragicomical history of thermodynamics 1822â1854
12174:. Since the 1990s, leading ecological economist and
9679:
Similarly at constant volume, the entropy change is:
6146:
The Boltzmann constant, and therefore entropy, have
5694:, specifically a thermodynamic state of the system.
5153:{\textstyle \Delta S_{{\mathsf {r}},i}=-Q_{i}/T_{i}}
3658:. A system composed of a pure substance of a single
3334:, which posited that in all heat-engines, whenever "
16241:(2nd ed.). Taylor and Francis (UK); CRC (US).
14553:Peter Atkins; Julio de Paula; James Keeler (2019).
13995:
13993:
13896:Moore, J. W.; C. L. Stanistski; P. C. Jurs (2005).
12964:. Dover Publications (still in print). p. 48.
12148:, made extensive use of the entropy concept in his
11788:{\textstyle \mathrm {d} U\rightarrow \mathrm {d} Q}
9270:
Isothermal expansion or compression of an ideal gas
6135:) that could cause the observed macroscopic state (
5350:
as the net heat into the inequality above gives us:
3429:, which is translated in an established lexicon as
16279:
16201:
16178:
16100:
15608:Cosmic Evolution: The Rise of Complexity in Nature
14926:(Expanded ed.). Singapore: World Scientific.
14919:
14115:
14113:
13969:
13897:
13697:
12821:
12677:
12657:
12622:
12355:
11972:
11952:
11927:
11902:
11787:
11751:
11731:
11703:
11683:
11659:
11622:
11602:
11507:
11467:
11432:
11328:
11217:
11139:
11097:
11064:
11035:
11006:
10886:
10859:
10827:
10800:
10780:
10760:
10740:
10720:
10693:
10539:
10506:
10477:
10448:
10375:
10219:
10135:
10102:
10015:
9970:
9874:
9764:
9735:
9664:
9628:
9561:
9541:
9498:
9474:
9454:
9364:
9344:
9324:
9297:
9250:
9199:
9152:
9132:
9105:
9085:
9049:
8986:
8926:
8882:
8845:
8809:
8773:
8695:
8540:
8520:
8499:
8479:
8459:
8439:
8419:
8377:
8346:
8326:
8289:
8257:
8219:
8109:
8082:
8059:
8012:
7992:
7965:
7828:
7798:
7688:
7668:
7609:
7589:
7565:
7504:
7477:
7447:
7416:
7393:
7302:
7237:
7179:
7006:As an example, for a glass of ice water in air at
6914:
6894:
6874:
6854:
6834:
6814:
6794:
6774:
6754:
6718:
6671:
6651:
6611:the fundamental postulate in statistical mechanics
6597:
6565:
6541:
6512:
6483:
6389:
6311:
6282:
6200:
6117:interpretation of entropy in statistical mechanics
6068:
6039:
6016:
5996:
5958:
5909:
5847:
5824:{\textstyle \int _{L}{\delta Q_{\mathsf {rev}}/T}}
5823:
5765:
5532:
5464:
5424:
5342:
5322:
5243:
5220:
5196:
5172:
5152:
5081:
4940:
4898:
4875:
4704:
4659:
4635:
4508:
4482:
4456:
4436:
4363:
4329:
4187:
4158:
4130:
4101:
4068:
4039:
4010:
3979:
3950:
3917:
3888:
3827:
3764:
3739:
3696:
3314:Fundamental Principles of Equilibrium and Movement
1956:
1886:
1218:
1163:
1108:
1053:
915:
891:
868:
844:
819:
783:
759:
736:
712:
687:
648:
624:
601:
577:
552:
16056:
15813:Ecological Economics. Principles and Applications
13348:(5th ed.). Oxford: Oxford University Press.
12890:. Mineola: Dover Publications. pp. 115â158.
12886:Clerk Maxwell, James (2001). Pesic, Peter (ed.).
12530:
12528:
11987:
7617:as the only external parameter, this relation is:
7363:, means that it is energetically more efficient.
5925:(J/K) in the International System of Units (SI).
5717:, for a reversible cyclic thermodynamic process:
4705:{\textstyle \mathrm {d} U=\delta Q-\mathrm {d} W}
3607:Graphical Methods in the Thermodynamics of Fluids
3369:in 1843, expresses the concept of energy and its
3302:(1822â1888), originator of the concept of entropy
18457:
16527:A primer on entropy tables for steam engineering
16200:Cutnell, John, D.; Johnson, Kenneth, J. (1998).
16098:
14882:
14830:
14607:. Cambridge University Press. pp. 500â501.
13990:
13782:"Reciprocal Relations in Irreversible Processes"
13003:
12161:integral part of the ecological economics school
11260:Entropy in thermodynamics and information theory
10237:
9251:{\displaystyle {\dot {S}}_{\mathsf {gen}}\geq 0}
7381:. The entropy change of a system at temperature
6004:of energy to the surrounding at the temperature
3365:, deduced from the heat-friction experiments of
16639:by Adam Shulman. Hour-long video, January 2013.
16599:Proof: S (or Entropy) is a valid state variable
16437:Fundamentals of statistical and thermal physics
15968:
15681:
15429:Srednicki M (August 1993). "Entropy and area".
15344:
15001:
14546:
14257:"Phase Equilibria & Colligative Properties"
14110:
12932:
12820:Carnot, Sadi Carnot (1986). Fox, Robert (ed.).
11242:). Using this concept, in conjunction with the
10897:
7337:
7303:{\textstyle U=\left\langle E_{i}\right\rangle }
7034:that is of great importance in the sciences of
3589:
16616:Moriarty, Philip; Merrifield, Michael (2009).
16609:Thermodynamic Entropy Definition Clarification
16512:(SpringerBriefs in Physics). Springer Nature.
16387:
16199:
16176:
14746:
14417:
14415:
14371:
14369:
14065:Late Nobel Laureate Max Born (8 August 2015).
13292:Physical chemistry : a molecular approach
13289:
12918:. Dover Publications. p. §90 & §137.
12525:
9994:) of a solid to a liquid at the melting point
9743:where the constant-volume molar heat capacity
8420:{\textstyle \mathrm {d} \theta /\mathrm {d} t}
6719:{\displaystyle S=k_{\mathsf {B}}\ln {\Omega }}
18476:Philosophy of thermal and statistical physics
17987:
17625:
16664:
16395:(2nd ed.). Singapore: World Scientific.
16322:Thermodynamics â A Dynamical Systems Approach
15923:"Economic de-growth vs. steady-state economy"
15764:
15729:. Cambridge, UK: Cambridge University Press.
14185:. GRC.nasa.gov. 27 March 2000. Archived from
13290:Simon, John D.; McQuarrie, Donald A. (1997).
13225:
13154:. San Francisco, CA: Addison Wesley. p.
13036:McGraw-Hill concise encyclopedia of chemistry
12909:
12907:
12885:
12799:(Online-Ausg. ed.). New York: Springer.
8359:of entry and exit of matter from the system.
8060:{\displaystyle \Delta G=\Delta H-T\ \Delta S}
7748:of substance, in which case it is called the
7100:
3617:, and the microscopic description central to
3201:including the transmission of information in
3131:
2676:
1759:
1693:
16643:The Second Law of Thermodynamics and Entropy
16577:Entropy and the Second Law of Thermodynamics
16500:: CS1 maint: multiple names: authors list (
16303:Thermodynamics. Foundations and Applications
16228:: CS1 maint: multiple names: authors list (
16168:: CS1 maint: multiple names: authors list (
15489:
15414:: CS1 maint: multiple names: authors list (
15149:: CS1 maint: multiple names: authors list (
14680:
14627:
14579:
14471:
14167:: CS1 maint: multiple names: authors list (
13999:
13283:
13118:
13116:
12926:
12447:: CS1 maint: multiple names: authors list (
11231:Mathematische Grundlagen der Quantenmechanik
11229:
9262:Entropy change formulas for simple processes
9050:{\textstyle \sum _{j}{{\dot {Q}}_{j}/T_{j}}}
7355:. As a result, there is no possibility of a
7187:and the entropy in classical thermodynamics:
6605:can be derived from it, but not vice versa.
6119:is the measure of uncertainty, disorder, or
6103:The statistical definition was developed by
3529:
3523:
3517:
3438:
3394:
1881:
1830:
15755:. In honor of John Wheeler's 90th birthday.
15428:
14412:
14366:
14347:
14291:Gribbin, John (1999). Gribbin, Mary (ed.).
14096:. New York: Academic Press. pp. 1â97.
13235:. Kluwer Academic: Dordrecht. pp. 1â22
13057:
13055:
12767:"6.5 Irreversibility, Entropy Changes, and
5582:
3486:(SI). Henceforth, the essential problem in
3424:
3267:into a new field of thermodynamics, called
3169:. It has found far-ranging applications in
17994:
17980:
17632:
17618:
16671:
16657:
16208:(4th ed.). John Wiley and Sons, Inc.
15819:(2nd ed.). Washington: Island Press.
15806:
15387:
14119:
13924:
13918:
13820:
13765:: CS1 maint: location missing publisher (
13252:
13250:
12904:
12828:. New York: Lilian Barber Press. pp.
12460:
12458:
12362:. New York: Springer-Verlag. p. 215.
10912:, the concept of entropy was developed by
10114:of a liquid to a gas at the boiling point
9772:is constant and there is no phase change.
9639:provided that the constant-pressure molar
7755:Thus, when one mole of substance at about
7485:is not available to do useful work, where
7401:absorbing an infinitesimal amount of heat
7377:places limits on a system's ability to do
3649:, in a sense that one state variable is a
3443:, a word often translated into English as
3423:, as in 'energy', and from the Greek word
3138:
3124:
2683:
2669:
1766:
1752:
1700:
1686:
98:
17639:
16364:Kroemer, Herbert; Charles Kittel (1980).
16084:(8th ed.). Oxford University Press.
15920:
15875:"On the practical limits to substitution"
15791:
15734:
15700:
15506:
15442:
15321:
15048:
14802:
14641:
14598:
14421:
14375:
14343:
14341:
14339:
14025:
13869:
13835:
13805:
13711:
13650:
13588:
13570:
13505:
13451:
13368:
13145:
13113:
13008:. Pearson Benjamin Cummings. p. 86.
12953:
12852:
12696:
12694:
12617:
12494:
12432:
12350:
9274:For the expansion (or compression) of an
8166:Entropy balance equation for open systems
8142:in 1986 to 295 (entropically compressed)
7030:Thermodynamic entropy is a non-conserved
3384:In the 1850s and 1860s, German physicist
16582:Khan Academy: entropy lectures, part of
16301:Gyftopoulos, E.P.; G.P. Beretta (2010).
16121:
15712:"Cosmic Inflation and the Arrow of Time"
15706:
15604:
14917:
14834:The Entropy Law and the Economic Process
14719:
14348:Brooks, Daniel R.; Wiley, E. O. (1988).
13611:
13605:
13555:"The Mathematics of the Ensemble Theory"
13422:
13343:
13052:
12613:
12611:
12534:
12464:
12380:
12152:The Entropy Law and the Economic Process
12125:Ecological economics § Methodology
10662:between equilibrium states was given by
10560:
9775:At low temperatures near absolute zero,
8957:In case of multiple heat flows the term
8447:in the system, equals the rate at which
8169:
7093:A special case of entropy increase, the
6962:
6951:
6208:of being occupied (usually given by the
6092:
4464:transferred in a thermodynamic process (
3294:
16409:
16368:(2nd ed.). W. H. Freeman Company.
16342:
16236:
16185:(6th ed.). New York: McGraw Hill.
15839:
15656:
15391:Informationâthe New Language of Science
14782:. Basel: BirkhĂ€user. pp. 119â144.
14582:"Book Review of 'A Science Miscellany'"
14559:. Oxford University Press. p. 89.
14505:
14472:Watson, J.R.; Carson, E.M. (May 2002).
14290:
14254:
14145:Chemical and Engineering Thermodynamics
14142:
13891:
13889:
13779:
13750:
13546:
13256:
13247:
12983:. Oxford University Press. p. 79.
12794:
12455:
12286:
11610:and if entropy is measured in units of
10547:is the "order" capacity of the system.
9200:{\textstyle {\dot {S}}_{\mathsf {gen}}}
8927:{\textstyle {\dot {S}}_{\mathsf {gen}}}
7763:, the sum of the incremental values of
7054:" machines; and second, it implies the
5465:{\textstyle \Delta S_{{\mathsf {r}},i}}
3331:Reflections on the Motive Power of Fire
18458:
17291:Integrated gasification combined cycle
16473:
16143:
16080:Atkins, Peter; Julio De Paula (2006).
15849:. Norwich: William Andrew Publishing.
15589:
15124:
14777:
14336:
14068:Natural Philosophy of Cause and Chance
13967:
13466:
13314:
13178:
13061:
13038:. New York: McGraw-Hill Professional.
13033:
13029:
13027:
13025:
12979:Atkins, Peter; Julio De Paula (2006).
12913:
12824:Reflexions on the motive power of fire
12819:
12700:
12691:
12629:. Princeton University Press. p.
12155:. Due to Georgescu-Roegen's work, the
11630:per nat, then the entropy is given by:
11481:probability, then that probability is
11169:
11089:
10942:
10531:
10498:
10469:
10438:
10426:
10404:
10401:
10398:
10395:
10392:
10365:
10353:
10337:
10334:
10331:
10328:
10325:
10322:
10319:
10316:
10209:
10196:
10193:
10190:
10169:
10166:
10163:
10127:
10089:
10076:
10073:
10070:
10049:
10046:
10043:
10007:
9517:
9236:
9233:
9230:
9191:
9188:
9185:
8918:
8915:
8912:
8686:
8683:
8680:
8249:
7957:
7954:
7951:
7948:
7945:
7942:
7924:
7921:
7918:
7915:
7912:
7909:
7906:
7903:
7900:
7897:
7894:
7891:
7873:
7870:
7867:
7864:
7861:
7858:
7855:
7852:
7782:
7779:
7776:
7542:The fundamental thermodynamic relation
7223:
7220:
7217:
7131:
6947:
6699:
6419:
6360:
6303:
6234:
6170:(SI unit: Jâ
Kâ
kg) or entropy per unit
5895:
5892:
5889:
5835:. Thus we can define a state function
5806:
5803:
5800:
5745:
5742:
5739:
5518:
5515:
5512:
5494:
5491:
5488:
5449:
5408:
5396:
5377:
5365:
5314:
5295:
5283:
5213:
5189:
5106:
5067:
5064:
5061:
5043:
5040:
5037:
5017:
5005:
4986:
4974:
4859:
4847:
4828:
4816:
4797:
4781:
4758:
4742:
4621:
4606:
4581:
4558:
4424:
4401:
4321:
4302:
4290:
4262:
4245:
4232:
4217:
4179:
4122:
4109:is greater than the magnitude of heat
4093:
4060:
4031:
3971:
3942:
3909:
3880:
3813:
3810:
3807:
3731:
3728:
3725:
3629:State variables and functions of state
17975:
17613:
17335:Radioisotope thermoelectric generator
17010:Quantum chromodynamics binding energy
16652:
16255:
16148:(2nd ed.). John Wiley and Sons.
16023:
15869:
15248:
15099:
14091:
13423:Ben-Naim, Arieh (21 September 2007).
13337:
13094:
12959:
12795:Lavenda, Bernard H. (2010). "2.3.4".
12645:Clausius coined the word entropy for
12608:
12311:
12109:the early rapid exponential expansion
11249:
10271:
9676:occurs in this temperature interval.
8258:{\textstyle {\dot {W}}_{\mathsf {S}}}
4941:{\textstyle \mathrm {d} S=\delta Q/T}
3740:{\textstyle \delta Q_{\mathsf {rev}}}
3673:
3346:. That was an early insight into the
17568:
16477:Physics for Scientists and Engineers
16459:. New York: Addison Wesley Longman.
16433:
15213:
14857:
14747:Tribus, M.; McIrvine, E. C. (1971).
14071:. BiblioLife. pp. 44, 146â147.
13886:
13395:
13229:Maximum Entropy and Bayesian Methods
9980:
7715:Thermodynamic entropy is central in
6925:Entropy can also be defined for any
6099:Entropy (statistical thermodynamics)
4716:and forms a central concept for the
18001:
17592:
17477:World energy supply and consumption
16571:Entropy and the Clausius inequality
16480:. Saunders Golden Subburst Series.
16278:Goldstein, Martin; Inge, F (1993).
14831:Georgescu-Roegen, Nicholas (1971).
14681:Carathéodory, C. (September 1909).
14506:Lambert, Frank L. (February 2002).
14456:
14207:
13552:
13097:The essential dictionary of science
13022:
13004:Engel, Thomas; Philip Reid (2006).
12797:A new perspective on thermodynamics
11284:regarding what name to give to the
10654:Entropy and adiabatic accessibility
10550:
10230:Approaches to understanding entropy
5969:From a macroscopic perspective, in
13:
18150:Evolutionary developmental biology
16531:vonBaeyer; Hans Christian (1998).
16049:
15990:10.1038/scientificamerican0905-100
15388:von Baeyer, Christian, H. (2003).
15053:An introduction to thermal physics
15008:Energy & Environmental Science
14319:"Entropy: Definition and Equation"
13753:An Introduction to Thermomechanics
13150:An introduction to thermal physics
12016:Philosophy and theoretical physics
11943:
11918:
11887:
11873:
11825:
11817:
11778:
11767:
11058:
11055:
10955:
10952:
10181:
10154:
10061:
10034:
9907:
9889:
9811:
9793:
9756:
9704:
9686:
9656:
9597:
9579:
9379:
8569:
8559:
8548:, the entropy balance equation is:
8528:of the extensive quantity entropy
8410:
8397:
8101:
8074:
8051:
8036:
8027:
7984:
7933:
7882:
7843:
7820:
7711:Entropy in chemical thermodynamics
7659:
7642:
7625:
7575:fundamental thermodynamic relation
7548:Fundamental thermodynamic relation
7375:fundamental thermodynamic relation
7316:generalized Boltzmann distribution
7247:fundamental thermodynamic relation
7195:
6712:
6666:
6646:
6535:
6532:
6432:
6429:
6060:
6031:
5988:
5867:
5589:Entropy (classical thermodynamics)
5503:
5479:
5439:
5432:or in terms of the entropy change
5096:
5052:
5028:
4914:
4695:
4675:
4534:
4383:
3855:The concept of entropy arose from
3785:
3687:
3437:and that he rendered in German as
2885:Evolutionary developmental biology
1917:
907:
860:
775:
728:
640:
593:
413:Intensive and extensive properties
16:Property of a thermodynamic system
14:
18502:
16553:
16282:The Refrigerator and the Universe
15684:Cosmology, Physics and Philosophy
14580:Sandra Saary (23 February 1993).
13836:Belkin, Andrey; et., al. (2015).
12739:
10916:and is generally referred to as "
10748:is defined as the largest number
7759:is warmed by its surroundings to
7705:relations between heat capacities
7424:in a reversible way, is given by
6976:Entropy arises directly from the
6882:. If observer B changes variable
1839:
17668:
17591:
17579:
17567:
17556:
17555:
16239:Entropy and its Physical Meaning
15962:
15914:
15863:
15833:
15800:
15758:
15675:
15650:
15634:Complexity and the Arrow of Time
15102:Information Theory and Evolution
13900:Chemistry, The Molecular Science
13375:. Harper & Row, Publishers.
13099:. New York: Barnes & Noble.
12598:habei ich absichtlich dem Worte
12594:des Körpers zu nennen. Das Wort
7799:{\textstyle q_{\mathsf {rev}}/T}
6336:the logarithm of the probability
5973:the entropy is interpreted as a
5558:the second law of thermodynamics
3991:compression stage. According to
3542:as a close parallel of the word
1669:
1668:
988:Table of thermodynamic equations
18284:Ordinary differential equations
16525:Entropy â A Basic Understanding
16457:Introduction to Thermal Physics
16024:David, Kover (14 August 2018).
15625:
15598:
15583:
15547:
15483:
15422:
15381:
15338:
15281:
15242:
15207:
15157:
15118:
15093:
15075:
15042:
14995:
14986:
14940:
14911:
14876:
14851:
14796:
14771:
14740:
14713:
14674:
14621:
14592:
14573:
14499:
14465:
14450:
14311:
14284:
14248:
14226:
14201:
14175:
14136:
14124:. IOP Publishing, Bristol, UK.
14085:
14058:
13961:
13829:
13814:
13773:
13744:
13691:
13630:
13494:The Journal of Chemical Physics
13485:
13460:
13416:
13389:
13362:
13308:
13219:
13172:
13139:
13088:
12997:
12972:
12879:
12861:. New York: Springer. pp.
12846:
12813:
12788:
12759:
12733:
12709:
12433:McCulloch, Richard, S. (1876).
12314:"General properties of entropy"
11305:, it was originally devised by
10136:{\displaystyle T_{\mathsf {b}}}
7536:
7531:local thermodynamic equilibrium
6802:and observer B using variables
3850:
3478:in this definition, called the
3052:Ordinary differential equations
1464:Maxwell's thermodynamic surface
18342:Partial differential equations
16107:. Cambridge University Press.
15900:10.1016/j.ecolecon.2006.02.011
15636:. Cambridge University Press.
15129:. Cambridge University Press.
14805:Science and Information Theory
14481:University Chemistry Education
13821:Kleidon, A.; et., al. (2005).
13181:"Gibbs vs Boltzmann Entropies"
12508:
12426:
12404:
12344:
12312:Wehrl, Alfred (1 April 1978).
12305:
12165:blemished somewhat by mistakes
11988:Interdisciplinary applications
11935:when a small amount of energy
11866:
11854:
11774:
11714:
11425:
11412:
11399:
11386:
11352:
11346:
11027:
10992:
10971:
10854:
10842:
10583:, and with the development of
8831:
8758:
8630:
7077:states that the entropy of an
7058:has the same direction as the
6504:
6469:
6448:
6338:that a microstate is occupied:
5773:which means the line integral
2923:Partial differential equations
2213:Atomic, molecular, and optical
1878:
1872:
1858:
1827:
1821:
1807:
1800:
1198:
1186:
1143:
1131:
1088:
1076:
1048:
1036:
1:
16455:Schroeder, Daniel V. (2000).
16393:Basics of Statistical Physics
15956:10.1016/j.jclepro.2009.10.019
15931:Journal of Cleaner Production
15921:Kerschner, Christian (2010).
15793:10.1016/s0921-8009(97)00079-7
15725:; Harper, Charles L. (eds.).
15275:10.1016/S0262-4079(21)00816-2
15049:Schroeder, Daniel V. (2000).
14660:10.1016/S0370-1573(98)00082-9
14512:Journal of Chemical Education
14143:Sandler, Stanley, I. (1989).
14120:Pokrovskii, Vladimir (2020).
13927:Journal of Chemical Education
13146:Schroeder, Daniel V. (2000).
12939:. J. Van Voorst. p. 28.
12541:Annalen der Physik und Chemie
12503:Annalen der Physik und Chemie
12299:
10910:quantum statistical mechanics
10238:Standard textbook definitions
9765:{\textstyle C_{\mathrm {V} }}
9665:{\textstyle C_{\mathrm {P} }}
9113:-th port into the system and
8427:, i.e. the rate of change of
8190:", i.e. those in which heat,
7455:. More explicitly, an energy
7082:entropy, in conjunction with
6542:{\displaystyle \mathrm {tr} }
6160:International System of Units
5575:, have to be consistent with
3929:expansion stage and the heat
3560:('tropy', 'transformation').
3552:('ergon', 'work') by that of
3484:International System of Units
3285:International System of Units
1365:Mechanical equivalent of heat
17655:Principle of maximum entropy
16474:Serway, Raymond, A. (1992).
16389:MĂŒller-Kirsten, Harald J. W.
16286:. Harvard University Press.
15974:"Economics for a Full World"
15611:. Harvard University Press.
15394:. Harvard University Press.
14837:. Harvard University Press.
14444:10.1016/0375-9601(84)90934-4
14255:Starzak, Michael E. (2010).
14236:. GRC.nasa.gov. 11 July 2008
13614:Oxford Dictionary of Physics
13257:Sandler, Stanley I. (2006).
13179:Jaynes, E. T. (1 May 1965).
12577:des Körpers, von der Gröƿse
12263:Principle of maximum entropy
12114:
12047:
11256:Entropy (information theory)
11098:{\textstyle k_{\mathsf {B}}}
10898:Entropy in quantum mechanics
10835:and a complementary amount,
10604:second law of thermodynamics
10540:{\textstyle C_{\mathsf {O}}}
10507:{\textstyle C_{\mathsf {I}}}
10478:{\textstyle C_{\mathsf {D}}}
10278:Entropy (order and disorder)
10016:{\textstyle T_{\mathsf {m}}}
8946:, internal heat transfer or
8127:Entropy (information theory)
7735:Thermodynamic entropy is an
7721:second law of thermodynamics
7344:second law of thermodynamics
7338:Second law of thermodynamics
7263:isothermalâisobaric ensemble
7075:second law of thermodynamics
6652:{\textstyle p_{i}=1/\Omega }
6312:{\textstyle k_{\mathsf {B}}}
6069:{\textstyle T\cdot \Delta S}
5699:second law of thermodynamics
4188:{\textstyle Q_{\mathsf {H}}}
4131:{\textstyle Q_{\mathsf {C}}}
4102:{\textstyle Q_{\mathsf {H}}}
4069:{\textstyle Q_{\mathsf {C}}}
4040:{\textstyle Q_{\mathsf {H}}}
3980:{\textstyle T_{\mathsf {C}}}
3951:{\textstyle Q_{\mathsf {C}}}
3918:{\textstyle T_{\mathsf {H}}}
3889:{\textstyle Q_{\mathsf {H}}}
3590:Definitions and descriptions
3505:
3348:second law of thermodynamics
3247:, and later coined the term
3235:. In 1865, German physicist
3210:second law of thermodynamics
977:Onsager reciprocal relations
7:
18092:Particle swarm optimization
16144:Callen, Herbert, B (2001).
15840:Schmitz, John E.J. (2007).
15657:Stenger, Victor J. (2007).
15367:10.1016/j.physa.2017.11.119
15193:10.1016/j.physa.2012.11.030
15125:Yockey, Hubert, P. (2005).
13755:. North Holland, Amsterdam.
13730:10.1016/j.physa.2014.05.014
13616:. Oxford University Press.
13185:American Journal of Physics
12619:Gillispie, Charles Coulston
12184:
12074:The entropy of a black hole
11036:{\textstyle {\hat {\rho }}}
10627:Relating entropy to energy
10613:first law of thermodynamics
9086:{\textstyle {\dot {Q}}_{j}}
8938:within the system, e.g. by
8846:{\textstyle {\hat {S}}_{k}}
8810:{\textstyle {\dot {M}}_{k}}
7015:the entropy has increased.
6969:temperatureâentropy diagram
6513:{\textstyle {\hat {\rho }}}
6177:Specifically, entropy is a
5934:third law of thermodynamics
4718:first law of thermodynamics
3363:first law of thermodynamics
3316:, the French mathematician
3165:, and to the principles of
2772:Particle swarm optimization
1469:Entropy as energy dispersal
1280:"Perpetual motion" machines
1219:{\displaystyle G(T,p)=H-TS}
1164:{\displaystyle A(T,V)=U-TS}
1109:{\displaystyle H(S,p)=U+pV}
10:
18507:
18337:Reaction-diffusion systems
18062:Self-organized criticality
17679:Statistical thermodynamics
16678:
16326:Princeton University Press
15659:God: The Failed Hypothesis
15605:Chaisson, Eric J. (2001).
15594:. Oxford University Press.
15461:10.1103/PhysRevLett.71.666
15251:"The cost of keeping time"
14588:. UAE: Galadari Press: xi.
14215:. ncsu.edu. Archived from
13972:Physical Chemistry, 5th ed
13669:10.1103/PhysRevE.80.011117
13590:10.1016/j.rinp.2022.105230
13321:Cambridge University Press
13315:Haynie, Donald T. (2001).
13095:Clark, John O. E. (2004).
12981:Physical Chemistry, 8th ed
12920:eqs.(39), (40), & (65)
12916:Treatise on Thermodynamics
12412:"Carnot, Sadi (1796â1832)"
12118:
12031:
11953:{\textstyle \mathrm {d} Q}
11928:{\textstyle \mathrm {d} S}
11660:{\displaystyle H=k\ln {W}}
11515:. The Shannon entropy (in
11253:
11065:{\textstyle \mathrm {tr} }
10901:
10648:heat death of the universe
10585:statistical thermodynamics
10557:Entropy (energy dispersal)
10554:
10275:
10250:at a specific temperature.
9140:is the temperature at the
8124:
7723:states that entropy in an
7545:
7101:Equivalence of definitions
6166:â either entropy per unit
6096:
5936:: perfect crystals at the
5586:
5565:statistical thermodynamics
5221:{\textstyle {\mathsf {C}}}
5197:{\textstyle {\mathsf {H}}}
4516:for a dissipation) we get:
3835:The reversible process is
3773:of the system during this
3697:{\textstyle \mathrm {d} S}
3554:
3548:
3538:, but preferring the term
3488:statistical thermodynamics
3454:Later, scientists such as
3305:
3290:
3208:Entropy is central to the
2919:Reactionâdiffusion systems
2748:Self-organized criticality
916:{\displaystyle \partial T}
869:{\displaystyle \partial V}
784:{\displaystyle \partial p}
737:{\displaystyle \partial V}
649:{\displaystyle \partial T}
602:{\displaystyle \partial S}
18:
18380:
18327:
18269:
18206:
18173:
18120:Artificial neural network
18105:
18030:
18009:
17914:
17876:
17841:
17796:
17738:
17677:
17666:
17647:
17551:
17525:
17401:
17281:Fossil fuel power station
17249:
17162:
17068:
16943:Electric potential energy
16908:
16888:Thermodynamic temperature
16868:Thermodynamic free energy
16863:Thermodynamic equilibrium
16709:
16686:
16419:. New York: A. A. Knopf.
16099:Baierlein, Ralph (2003).
15810:; Farley, Joshua (2011).
15768:; Ruth, Matthias (1997).
15226:10.1007/978-1-4939-3466-9
14897:10.1007/s11018-005-0195-9
14147:. John Wiley & Sons.
13553:Gao, Xiang (March 2022).
13317:Biological Thermodynamics
13062:Sethna, James P. (2006).
12535:Clausius, Rudolf (1865).
12338:10.1103/RevModPhys.50.221
12318:Reviews of Modern Physics
12134:Nicholas Georgescu-Roegen
11669:Boltzmann entropy formula
10860:{\textstyle (1-\lambda )}
10594:Ambiguities in the terms
9569:, the entropy change is:
9482:is the amount of gas (in
9093:is the heat flow through
8987:{\textstyle {\dot {Q}}/T}
8883:{\textstyle {\dot {Q}}/T}
8356:thermodynamic temperature
8327:{\textstyle {\dot {Q}}/T}
8265:and pressure-volume work
6079:thermodynamic equilibrium
5701:, entropy of an isolated
5676:thermodynamic equilibrium
5330:Substitution of the work
4138:. Through the efforts of
3639:thermodynamic equilibrium
3425:
3265:probability distributions
3214:thermodynamic equilibrium
2860:Artificial neural network
1390:An Inquiry Concerning the
73:
63:
51:
46:
18198:Evolutionary game theory
18125:Evolutionary computation
18057:Collective consciousness
17939:Condensed matter physics
17922:Statistical field theory
17352:Concentrated solar power
16637:The Discovery of Entropy
16630:University of Nottingham
16065:. Vieweg, Braunschweig.
15817:(PDF contains full book)
15682:Benjamin Gal-Or (1987).
15525:10.1103/PhysRevE.53.3738
15249:Crane, Leah (May 2021).
14918:Ben-Naim, Arieh (2008).
14803:Brillouin, Leon (1956).
14749:"Energy and information"
14297:. New York: Free Press.
13467:Callen, Herbert (2001).
13369:de Rosnay, Joel (1979).
13134:Probabilities in Physics
13034:Licker, Mark D. (2004).
12933:Rudolf Clausius (1867).
12701:Cooper, Leon N. (1968).
12573:gesagt ist, sie sey der
12561:10.1002/andp.18652010702
12487:10.1002/andp.18501550306
12414:. Wolfram Research. 2007
12279:
12163:. Although his work was
11293:When viewed in terms of
11114:correspondence principle
10581:classical thermodynamics
10256:a measure of a system's
9672:is constant and that no
8290:{\textstyle P{\dot {V}}}
7752:with a unit of Jâ
molâ
K.
7259:grand canonical ensemble
7003:) than any other state.
6608:In what has been called
5997:{\displaystyle \Delta E}
5971:classical thermodynamics
5583:Classical thermodynamics
4345:It is known that a work
3641:, which essentially are
3635:thermodynamic properties
3615:classical thermodynamics
3476:proportionality constant
3277:proportionality constant
3159:classical thermodynamics
3111:Evolutionary game theory
3001:Second-order cybernetics
2865:Evolutionary computation
2781:Collective consciousness
1970:Einstein field equations
1403:Heterogeneous Substances
820:{\displaystyle \alpha =}
688:{\displaystyle \beta =-}
34:Not to be confused with
22:Entropy (disambiguation)
18216:Social network analysis
18155:Artificial intelligence
18087:Ant colony optimization
18047:Collective intelligence
17797:Mathematical approaches
17786:Lennard-Jones potential
17702:thermodynamic potential
16893:Volume (thermodynamics)
16873:Thermodynamic potential
16776:Massâenergy equivalence
16237:Dugdale, J. S. (1996).
16177:Chang, Raymond (1998).
14323:EncyclopĂŠdia Britannica
14027:10.1126/science.1200970
13825:. Heidelberg: Springer.
13612:Daintith, John (2005).
13471:. John Wiley and Sons.
13346:A dictionary of science
13344:Daintith, John (2005).
12393:, Elsevier, Amsterdam,
12273:Thermodynamic potential
10672:Constantin Carathéodory
10660:adiabatic accessibility
10145:entropy of vaporization
9549:to a final temperature
9278:from an initial volume
8220:{\textstyle {\dot {Q}}}
8117:is the entropy change.
7717:chemical thermodynamics
7577:. If external pressure
7448:{\textstyle \delta q/T}
7251:microcanonical ensemble
6728:microcanonical ensemble
6024:, its entropy falls by
5204:for a hot reservoir or
3500:Constantin Carathéodory
3227:in 1850 with the names
2889:Artificial intelligence
2803:Social network analysis
2768:Ant colony optimization
2740:Collective intelligence
2273:Theories of gravitation
2188:Electroweak interaction
69:joules per kelvin (Jâ
K)
29:Introduction to entropy
18347:Dissipative structures
18188:Rational choice theory
17833:conformal field theory
16848:Quantum thermodynamics
16838:Laws of thermodynamics
16719:Conservation of energy
16523:Spirax-Sarco Limited,
16343:Johnson, Eric (2018).
15590:Layzer, David (1990).
15562:. Wiley. p. 162.
14885:Measurement Techniques
14807:. Dover Publications.
13968:Levine, I. N. (2002).
13807:10.1103/PhysRev.37.405
13780:Onsager, Lars (1931).
13128:13 August 2011 at the
12853:Truesdell, C. (1980).
12705:. Harper. p. 331.
12679:
12659:
12501: : Poggendorff's
12222:Entropic value at risk
12207:Conformational entropy
12157:laws of thermodynamics
11974:
11954:
11929:
11904:
11789:
11753:
11733:
11705:
11685:
11661:
11624:
11604:
11555:
11509:
11469:
11434:
11381:
11330:
11273:
11240:projective measurement
11236:wave function collapse
11230:
11219:
11141:
11099:
11066:
11037:
11008:
10888:
10861:
10829:
10802:
10782:
10762:
10742:
10722:
10695:
10576:
10541:
10508:
10479:
10450:
10377:
10221:
10137:
10104:
10017:
9972:
9876:
9766:
9737:
9666:
9630:
9563:
9543:
9500:
9476:
9456:
9366:
9346:
9326:
9299:
9252:
9201:
9154:
9134:
9107:
9087:
9051:
8988:
8928:
8884:
8847:
8811:
8775:
8730:
8697:
8602:
8542:
8522:
8501:
8481:
8461:
8441:
8421:
8379:
8348:
8328:
8291:
8259:
8221:
8179:
8111:
8084:
8061:
8014:
7994:
7967:
7830:
7800:
7690:
7670:
7611:
7591:
7567:
7506:
7479:
7449:
7418:
7395:
7304:
7267:Boltzmann distribution
7239:
7181:
7067:standard molar entropy
6973:
6960:
6942:Lectures on Gas Theory
6916:
6896:
6876:
6856:
6836:
6816:
6796:
6776:
6756:
6720:
6673:
6653:
6616:degenerate microstates
6599:
6567:
6543:
6514:
6485:
6391:
6313:
6284:
6210:Boltzmann distribution
6202:
6070:
6041:
6018:
5998:
5960:
5911:
5849:
5825:
5767:
5534:
5466:
5426:
5344:
5324:
5245:
5222:
5198:
5174:
5154:
5083:
4942:
4900:
4877:
4706:
4661:
4637:
4510:
4490:for an absorption and
4484:
4458:
4438:
4365:
4331:
4189:
4160:
4132:
4103:
4070:
4041:
4012:
3981:
3952:
3919:
3890:
3829:
3766:
3741:
3698:
3599:
3581:
3530:
3524:
3518:
3439:
3395:
3391:transformation-content
3303:
3251:from a Greek word for
3241:transformation-content
3229:thermodynamic function
3102:Rational choice theory
2927:Dissipative structures
1958:
1888:
1220:
1165:
1110:
1055:
1054:{\displaystyle U(S,V)}
917:
893:
870:
846:
821:
785:
761:
738:
714:
689:
650:
626:
603:
579:
554:
533:Specific heat capacity
137:Quantum thermodynamics
18160:Evolutionary robotics
18077:Agent-based modelling
17748:Ferromagnetism models
17641:Statistical mechanics
16965:Interatomic potential
16756:Energy transformation
14687:Mathematische Annalen
12680:
12660:
12575:WĂ€rme- und Werkinhalt
12522:, pp. 1826â1827.
12202:Configuration entropy
12176:steady-state theorist
11975:
11955:
11930:
11905:
11790:
11754:
11734:
11706:
11686:
11662:
11625:
11605:
11535:
11510:
11470:
11435:
11361:
11331:
11288:in phone-line signals
11276:Conversation between
11268:
11220:
11142:
11100:
11067:
11038:
11009:
10889:
10862:
10830:
10803:
10801:{\textstyle \lambda }
10783:
10763:
10761:{\textstyle \lambda }
10743:
10723:
10696:
10573:
10542:
10509:
10480:
10451:
10378:
10222:
10138:
10105:
10018:
9973:
9877:
9767:
9738:
9667:
9631:
9564:
9544:
9501:
9477:
9457:
9367:
9347:
9327:
9300:
9253:
9202:
9155:
9135:
9108:
9088:
9052:
8989:
8929:
8885:
8848:
8812:
8776:
8710:
8698:
8582:
8543:
8523:
8502:
8482:
8462:
8442:
8422:
8380:
8349:
8329:
8292:
8260:
8227:, flow of shaft work
8222:
8173:
8112:
8110:{\textstyle \Delta S}
8085:
8083:{\textstyle \Delta H}
8062:
8015:
7995:
7993:{\textstyle \Delta G}
7968:
7831:
7829:{\textstyle \Delta S}
7801:
7691:
7671:
7612:
7592:
7568:
7507:
7480:
7450:
7419:
7417:{\textstyle \delta q}
7396:
7312:Gibbs entropy formula
7305:
7240:
7182:
7107:Gibbs entropy formula
6966:
6955:
6917:
6897:
6877:
6857:
6837:
6817:
6797:
6777:
6757:
6721:
6674:
6654:
6600:
6568:
6544:
6515:
6486:
6392:
6314:
6285:
6203:
6093:Statistical mechanics
6071:
6042:
6040:{\textstyle \Delta S}
6019:
5999:
5961:
5912:
5850:
5826:
5768:
5535:
5467:
5427:
5345:
5325:
5246:
5223:
5199:
5175:
5155:
5084:
4943:
4901:
4878:
4707:
4662:
4638:
4511:
4485:
4459:
4439:
4366:
4332:
4190:
4161:
4133:
4104:
4071:
4042:
4013:
3982:
3953:
3920:
3891:
3830:
3767:
3742:
3699:
3651:mathematical function
3619:statistical mechanics
3594:
3565:
3531:WĂ€rme- und Werkinhalt
3298:
3269:statistical mechanics
3030:Theory of computation
2893:Evolutionary robotics
2760:Agent-based modelling
2151:Philosophy of physics
1959:
1889:
1401:On the Equilibrium of
1221:
1166:
1119:Helmholtz free energy
1111:
1056:
918:
894:
871:
847:
822:
786:
762:
739:
715:
690:
651:
627:
604:
580:
555:
18491:Extensive quantities
18319:Coupled map lattices
18279:Time series analysis
18221:Small-world networks
17413:Efficient energy use
17386:Airborne wind energy
17364:Solar thermal energy
17271:Electricity delivery
16883:Thermodynamic system
16828:Irreversible process
16129:. World Scientific.
15883:Ecological Economics
15775:Ecological Economics
15766:Cleveland, Cutler J.
15661:. Prometheus Books.
15104:. World Scientific.
15100:Avery, John (2003).
14862:. World Scientific.
14726:. Elsevier Science.
13751:Ziegler, H. (1983).
12669:
12649:
12146:ecological economics
12006:ecological economics
11964:
11939:
11914:
11799:
11763:
11743:
11739:and constant volume
11723:
11695:
11675:
11634:
11614:
11523:
11485:
11459:
11340:
11313:
11264:Entropic uncertainty
11151:
11124:
11080:
11051:
11018:
10924:
10871:
10839:
10812:
10792:
10772:
10752:
10732:
10705:
10678:
10664:E. H. Lieb
10522:
10489:
10460:
10387:
10311:
10296:thermodynamic system
10151:
10118:
10031:
9998:
9886:
9790:
9747:
9683:
9647:
9576:
9553:
9526:
9490:
9466:
9376:
9356:
9336:
9309:
9282:
9212:
9167:
9144:
9117:
9097:
9061:
8998:
8961:
8894:
8857:
8821:
8785:
8707:
8552:
8532:
8512:
8500:{\textstyle \theta }
8491:
8480:{\textstyle \theta }
8471:
8460:{\textstyle \theta }
8451:
8440:{\textstyle \theta }
8431:
8393:
8387:thermodynamic system
8378:{\textstyle \theta }
8369:
8338:
8301:
8269:
8231:
8202:
8184:chemical engineering
8098:
8071:
8024:
8004:
7981:
7840:
7817:
7767:
7680:
7621:
7601:
7597:bears on the volume
7581:
7557:
7489:
7459:
7428:
7405:
7385:
7273:
7191:
7113:
7025:thermodynamic system
6985:thermodynamic system
6958:thermodynamic system
6940:In Boltzmann's 1896
6906:
6886:
6866:
6846:
6826:
6806:
6786:
6766:
6746:
6684:
6672:{\textstyle \Omega }
6663:
6622:
6589:
6566:{\displaystyle \ln }
6557:
6528:
6495:
6401:
6342:
6294:
6216:
6185:
6174:(SI unit: Jâ
Kâ
mol).
6083:chemical equilibrium
6051:
6028:
6008:
5985:
5979:thermodynamic system
5944:
5863:
5839:
5777:
5721:
5688:absolute temperature
5476:
5436:
5354:
5334:
5255:
5235:
5208:
5184:
5164:
5093:
4960:
4910:
4890:
4727:
4671:
4651:
4520:
4494:
4468:
4448:
4375:
4349:
4199:
4170:
4150:
4113:
4084:
4051:
4022:
4002:
3962:
3933:
3900:
3871:
3781:
3756:
3713:
3683:
3460:Josiah Willard Gibbs
3401:thermodynamic system
3081:Coupled map lattices
3047:Time series analysis
2807:Small-world networks
2283:Theory of everything
2161:Quantum field theory
1898:
1791:
1414:Motive Power of Fire
1180:
1125:
1070:
1030:
982:Bridgman's equations
959:Fundamental relation
904:
883:
857:
836:
808:
772:
751:
725:
704:
673:
637:
616:
590:
569:
541:
20:For other uses, see
18471:Physical quantities
18299:Population dynamics
18193:Bounded rationality
18135:Genetic programming
17927:elementary particle
17692:partition functions
17435:Energy conservation
17357:Photovoltaic system
17330:Nuclear power plant
17015:Quantum fluctuation
16878:Thermodynamic state
16853:Thermal equilibrium
16508:Sharp, Kim (2019).
16382:Lambert, Frank L.;
16127:Entropy Demystified
15978:Scientific American
15948:2010JCPro..18..544K
15745:2002astro.ph.10527A
15686:. Springer Verlag.
15517:1996PhRvE..53.3738C
15453:1993PhRvL..71..666S
15359:2018PhyA..493..444T
15306:2015NatSR...5E7611C
15267:2021NewSc.250...15C
15214:Chen, Jing (2015).
15185:2013PhyA..392.1122C
15083:"Measuring Entropy"
14975:jibberish [
14858:Chen, Jing (2005).
14753:Scientific American
14652:1999PhR...310....1L
14524:2002JChEd..79..187L
14436:1984PhLA..102..171L
14390:1984JSP....35..159L
14130:2020tcsp.book.....P
14018:2011Sci...332...60H
13939:2006JChEd..83.1686J
13854:2015NatSR...5E8323B
13798:1931PhRv...37..405O
13722:2014PhyA..410...17M
13661:2009PhRvE..80a1117S
13581:2022ResPh..3405230G
13516:2019JChPh.151c4113G
13444:2007Entrp...9..132B
13197:1965AmJPh..33..391J
12914:Planck, M. (1945).
12581:sagen, sie sey der
12553:1865AnP...201..353C
12479:1850AnP...155..368C
12330:1978RvMP...50..221W
12172:'entropy pessimism'
12140:in economics and a
10918:von Neumann entropy
10904:von Neumann entropy
9782:Since entropy is a
9643:(or specific heat)
9518:Cooling and heating
7478:{\textstyle T_{R}S}
6948:Entropy of a system
6931:reversible dynamics
6172:amount of substance
6087:standard conditions
5597:Conjugate variables
4509:{\textstyle Q<0}
4483:{\textstyle Q>0}
4364:{\textstyle W>0}
3865:thermodynamic cycle
3678:The entropy change
3498:identical systems.
3464:James Clerk Maxwell
3411:during a change of
3258:Austrian physicist
3199:information systems
3163:statistical physics
3106:Bounded rationality
3064:Population dynamics
2973:Conversation theory
2873:Genetic programming
2798:Scale-free networks
2730:Collective behavior
2233:Non-linear dynamics
2171:Quantum computation
2166:Quantum information
2040:Satyendra Nath Bose
1740:Statistical entropy
1392:Source ... Friction
1324:Loschmidt's paradox
516:Material properties
394:Conjugate variables
18445:Computation theory
18440:Information theory
18395:Operationalization
18271:Nonlinear dynamics
18183:Prisoner's dilemma
18130:Genetic algorithms
17954:information theory
17861:correlation length
17856:Critical exponents
17843:Critical phenomena
17824:stochastic process
17804:Boltzmann equation
17697:equations of state
17472:Sustainable energy
17450:Energy development
17440:Energy consumption
17276:Energy engineering
16584:Chemistry playlist
16082:Physical Chemistry
15294:Scientific Reports
15020:10.1039/C9EE02964H
14699:10.1007/BF01450409
14457:Lambert, Frank L.
14398:10.1007/bf01017372
14092:Haase, R. (1971).
13947:10.1021/ed083p1686
13842:Scientific Reports
13559:Results in Physics
13006:Physical Chemistry
12960:Fermi, E. (1956).
12742:"What is entropy?"
12675:
12655:
12583:Verwandlungsinhalt
12496:2027/uc1.$ b242250
12467:Annalen der Physik
12437:. D. Van Nostrand.
12254:(negative entropy)
12212:Entropic explosion
12064:has pointed out â
11994:information theory
11970:
11950:
11925:
11900:
11785:
11749:
11729:
11701:
11681:
11657:
11620:
11600:
11508:{\textstyle p=1/W}
11505:
11465:
11430:
11329:{\textstyle p_{i}}
11326:
11295:information theory
11250:Information theory
11215:
11184:
11140:{\textstyle p_{i}}
11137:
11107:Boltzmann constant
11095:
11062:
11033:
11004:
10887:{\textstyle X_{0}}
10884:
10857:
10828:{\textstyle X_{1}}
10825:
10798:
10778:
10758:
10738:
10721:{\textstyle X_{1}}
10718:
10694:{\textstyle X_{0}}
10691:
10621:Physical Chemistry
10619:, in his textbook
10577:
10537:
10504:
10475:
10446:
10373:
10304:information theory
10272:Order and disorder
10217:
10133:
10100:
10013:
9968:
9872:
9762:
9733:
9662:
9626:
9559:
9542:{\textstyle T_{0}}
9539:
9512:throttling process
9508:ideal gas constant
9496:
9472:
9452:
9362:
9342:
9332:to a final volume
9325:{\textstyle P_{0}}
9322:
9298:{\textstyle V_{0}}
9295:
9248:
9197:
9150:
9133:{\textstyle T_{j}}
9130:
9103:
9083:
9047:
9010:
8984:
8948:frictional effects
8940:chemical reactions
8936:entropy generation
8924:
8880:
8843:
8807:
8771:
8693:
8538:
8518:
8497:
8477:
8457:
8437:
8417:
8375:
8364:extensive quantity
8344:
8324:
8287:
8255:
8217:
8180:
8107:
8080:
8057:
8010:
7990:
7963:
7826:
7796:
7741:intensive property
7686:
7666:
7607:
7587:
7563:
7505:{\textstyle T_{R}}
7502:
7475:
7445:
7414:
7391:
7300:
7255:canonical ensemble
7249:are known for the
7245:together with the
7235:
7177:
7146:
6974:
6961:
6912:
6892:
6872:
6852:
6832:
6812:
6792:
6772:
6752:
6716:
6669:
6649:
6595:
6563:
6539:
6510:
6481:
6387:
6321:Boltzmann constant
6309:
6280:
6249:
6201:{\textstyle p_{i}}
6198:
6164:intensive property
6141:Boltzmann constant
6110:Boltzmann constant
6089:is well-defined).
6066:
6037:
6014:
5994:
5956:
5907:
5845:
5821:
5763:
5650:Chemical potential
5577:quantum statistics
5573:photovoltaic cells
5530:
5462:
5422:
5340:
5320:
5241:
5218:
5194:
5170:
5150:
5079:
4938:
4896:
4873:
4712:. It is called an
4702:
4657:
4633:
4506:
4480:
4454:
4434:
4361:
4327:
4185:
4156:
4128:
4099:
4066:
4037:
4008:
3977:
3948:
3915:
3886:
3825:
3762:
3737:
3694:
3674:Reversible process
3525:Verwandlungsinhalt
3480:Boltzmann constant
3396:Verwandlungsinhalt
3322:moment of activity
3312:In his 1803 paper
3308:History of entropy
3304:
3281:Boltzmann constant
3245:Verwandlungsinhalt
3167:information theory
3097:Prisoner's dilemma
3042:Nonlinear dynamics
2997:Operationalization
2993:Information theory
2869:Genetic algorithms
2258:General relativity
2253:Special relativity
2193:Strong interaction
1954:
1884:
1656:Order and disorder
1412:Reflections on the
1319:Heat death paradox
1216:
1161:
1106:
1051:
913:
889:
866:
842:
817:
781:
757:
734:
710:
685:
646:
622:
599:
575:
553:{\displaystyle c=}
550:
523:Property databases
499:Reduced properties
483:Chemical potential
447:Functions of state
370:Thermal efficiency
106:Carnot heat engine
77:SI base units
18453:
18452:
18357:Cellular automata
18329:Pattern formation
18261:Adaptive networks
18052:Collective action
18022:Self-organization
17969:
17968:
17959:Boltzmann machine
17829:mean-field theory
17730:Maxwell relations
17607:
17606:
17374:Solar power tower
17020:Quantum potential
16858:Thermal reservoir
16761:Energy transition
16589:Entropy Intuition
16544:978-0-679-43342-2
16487:978-0-03-096026-0
16466:978-0-201-38027-9
16447:978-0-07-051800-1
16434:Reif, F. (1965).
16426:978-0-679-45443-4
16402:978-981-4449-53-3
16375:978-0-7167-1088-2
16356:978-0-262-03861-4
16349:. The MIT Press.
16335:978-0-691-12327-1
16312:978-0-486-43932-7
16293:978-0-674-75325-9
16270:978-0-486-60361-2
16263:. Prentice Hall.
16248:978-0-7484-0569-5
16215:978-0-471-19113-1
16192:978-0-07-115221-1
16155:978-0-471-86256-7
16136:978-981-270-055-1
16114:978-0-521-65838-6
16091:978-0-19-870072-2
16072:978-3-528-33311-9
15856:978-0-8155-1537-1
15826:978-1-59726-681-9
15723:Davies, Paul C.W.
15708:Albrecht, Andreas
15693:978-0-387-96526-0
15668:978-1-59102-481-1
15643:978-1-107-02725-1
15618:978-0-674-00342-2
15401:978-0-674-01387-2
15314:10.1038/srep07611
15235:978-1-4939-3464-5
15136:978-0-521-80293-2
15111:978-981-238-399-0
15068:978-0-201-38027-9
14869:978-981-256-323-1
14844:978-0-674-25781-8
14814:978-0-486-43918-1
14789:978-3-7643-7116-6
14733:978-1-4831-8491-3
14720:R. Giles (2016).
14614:978-0-521-26173-9
14566:978-0-19-882336-0
14532:10.1021/ed079p187
14359:978-0-226-07574-7
14304:978-0-684-85578-3
14208:Franzen, Stefan.
14189:on 21 August 2011
14154:978-0-471-83050-4
14103:978-0-12-245601-5
14078:978-1-298-49740-6
13983:978-0-07-231808-1
13933:(11): 1686â1694.
13911:978-0-534-42201-1
13862:10.1038/srep08323
13639:Physical Review E
13623:978-0-19-280628-4
13524:10.1063/1.5111333
13478:978-0-471-86256-7
13404:on 19 August 2012
13398:"Heat Capacities"
13382:978-0-06-011029-1
13355:978-0-19-280641-3
13330:978-0-521-79165-6
13301:978-0-935702-99-6
13276:978-0-471-66174-0
13205:10.1119/1.1971557
13165:978-0-201-38027-9
13106:978-0-7607-4616-5
13081:978-0-19-856677-9
13045:978-0-07-143953-4
13015:978-0-8053-3842-3
12990:978-0-19-870072-2
12946:978-1-4981-6733-8
12897:978-0-486-41735-6
12872:978-0-387-90403-0
12839:978-0-936508-16-0
12806:978-1-4419-1430-9
12678:{\displaystyle S}
12658:{\displaystyle S}
12192:Boltzmann entropy
12130:Romanian American
12111:of the universe.
12091:Hawking radiation
11898:
11871:
11865:
11859:
11853:
11832:
11175:
11116:, because in the
11112:This upholds the
11030:
10995:
10974:
10950:
10571:
10444:
10371:
10215:
10095:
10025:entropy of fusion
9987:phase transitions
9981:Phase transitions
9966:
9934:
9870:
9838:
9731:
9624:
9450:
9415:
9225:
9180:
9074:
9022:
9001:
8973:
8944:phase transitions
8907:
8869:
8834:
8798:
8761:
8742:
8675:
8660:
8655:
8633:
8614:
8577:
8313:
8284:
8244:
8214:
8050:
7975:Gibbs free energy
7729:Clausius equation
7701:Maxwell relations
7657:
7640:
7527:equilibrium state
7361:chemical reaction
7351:, which performs
7349:adiabatic cooling
7233:
7137:
7095:entropy of mixing
6989:equilibrium state
6735:equilibrium state
6507:
6472:
6451:
6427:
6240:
6123:in the phrase of
5905:
5755:
5715:Clausius equality
5713:According to the
5692:function of state
5664:
5663:
5660:
5659:
5599:of thermodynamics
5414:
5383:
5301:
5023:
4992:
4906:with a change of
4865:
4834:
4803:
4764:
4667:with a change of
4308:
4251:
3823:
3534:) as the name of
3472:natural logarithm
3399:in German), of a
3203:telecommunication
3148:
3147:
2935:Cellular automata
2909:Pattern formation
2840:Adaptive networks
2744:Collective action
2713:Self-organization
2693:
2692:
2156:Quantum mechanics
2030:Ernest Rutherford
2010:Erwin Schrödinger
2005:Werner Heisenberg
1855:
1803:
1776:
1775:
1735:Classical entropy
1710:
1709:
1651:Self-organization
1476:
1475:
1174:Gibbs free energy
972:Maxwell relations
930:
929:
926:
925:
892:{\displaystyle V}
845:{\displaystyle 1}
800:Thermal expansion
794:
793:
760:{\displaystyle V}
713:{\displaystyle 1}
659:
658:
625:{\displaystyle N}
578:{\displaystyle T}
506:
505:
422:Process functions
408:Property diagrams
387:System properties
377:
376:
342:Endoreversibility
234:Equation of state
86:
85:
18498:
18367:Self-replication
18256:Dynamic networks
18145:Machine learning
18072:Phase transition
17996:
17989:
17982:
17973:
17972:
17851:Phase transition
17672:
17671:
17634:
17627:
17620:
17611:
17610:
17595:
17594:
17583:
17571:
17570:
17559:
17558:
17533:Carbon footprint
17467:Renewable energy
17308:Hydroelectricity
17298:Geothermal power
16741:Energy condition
16673:
16666:
16659:
16650:
16649:
16633:
16548:
16537:. Random House.
16505:
16499:
16491:
16470:
16451:
16430:
16406:
16379:
16360:
16339:
16316:
16297:
16285:
16274:
16252:
16233:
16227:
16219:
16207:
16196:
16184:
16173:
16167:
16159:
16140:
16125:, Arieh (2007).
16118:
16106:
16095:
16076:
16045:
16043:
16041:
16032:. Archived from
16017:
16016:
16014:
16012:
15966:
15960:
15959:
15938:(6). Amsterdam:
15927:
15918:
15912:
15911:
15879:
15871:Ayres, Robert U.
15867:
15861:
15860:
15848:
15837:
15831:
15830:
15818:
15804:
15798:
15797:
15795:
15782:(3). Amsterdam:
15762:
15756:
15754:
15753:
15751:
15738:
15736:astro-ph/0210527
15716:
15704:
15698:
15697:
15679:
15673:
15672:
15654:
15648:
15647:
15629:
15623:
15622:
15602:
15596:
15595:
15587:
15581:
15580:
15578:
15576:
15551:
15545:
15544:
15510:
15508:cond-mat/9601111
15501:(4): 3738â3744.
15487:
15481:
15480:
15446:
15426:
15420:
15419:
15413:
15405:
15385:
15379:
15378:
15342:
15336:
15335:
15325:
15285:
15279:
15278:
15246:
15240:
15239:
15211:
15205:
15204:
15179:(5): 1122â1132.
15170:
15161:
15155:
15154:
15148:
15140:
15122:
15116:
15115:
15097:
15091:
15090:
15079:
15073:
15072:
15056:
15046:
15040:
15039:
14999:
14993:
14990:
14984:
14983:
14971:
14969:
14944:
14938:
14937:
14925:
14915:
14909:
14908:
14880:
14874:
14873:
14855:
14849:
14848:
14828:
14819:
14818:
14800:
14794:
14793:
14775:
14769:
14768:
14744:
14738:
14737:
14717:
14711:
14710:
14678:
14672:
14671:
14645:
14643:cond-mat/9708200
14625:
14619:
14618:
14599:Smith, Crosbie;
14596:
14590:
14589:
14577:
14571:
14570:
14550:
14544:
14543:
14503:
14497:
14496:
14478:
14469:
14463:
14462:
14454:
14448:
14447:
14419:
14410:
14409:
14384:(1â2): 159â169.
14378:J. Stat. Physics
14373:
14364:
14363:
14345:
14334:
14333:
14331:
14329:
14315:
14309:
14308:
14288:
14282:
14281:
14279:
14277:
14252:
14246:
14245:
14243:
14241:
14230:
14224:
14223:
14221:
14214:
14205:
14199:
14198:
14196:
14194:
14179:
14173:
14172:
14166:
14158:
14140:
14134:
14133:
14117:
14108:
14107:
14089:
14083:
14082:
14062:
14056:
14055:
14029:
13997:
13988:
13987:
13975:
13965:
13959:
13958:
13922:
13916:
13915:
13903:
13893:
13884:
13883:
13873:
13833:
13827:
13826:
13818:
13812:
13811:
13809:
13777:
13771:
13770:
13764:
13756:
13748:
13742:
13741:
13715:
13695:
13689:
13688:
13654:
13634:
13628:
13627:
13609:
13603:
13602:
13592:
13574:
13550:
13544:
13543:
13509:
13489:
13483:
13482:
13464:
13458:
13457:
13455:
13453:10.3390/e9030133
13429:
13420:
13414:
13413:
13411:
13409:
13400:. Archived from
13396:McGovern, J. A.
13393:
13387:
13386:
13366:
13360:
13359:
13341:
13335:
13334:
13312:
13306:
13305:
13287:
13281:
13280:
13264:
13254:
13245:
13244:
13242:
13240:
13234:
13223:
13217:
13216:
13176:
13170:
13169:
13153:
13143:
13137:
13120:
13111:
13110:
13092:
13086:
13085:
13069:
13059:
13050:
13049:
13031:
13020:
13019:
13001:
12995:
12994:
12976:
12970:
12968:
12957:
12951:
12950:
12930:
12924:
12922:
12911:
12902:
12901:
12883:
12877:
12876:
12860:
12850:
12844:
12843:
12827:
12817:
12811:
12810:
12792:
12786:
12785:
12783:
12781:
12763:
12757:
12756:
12754:
12752:
12740:Lower, Stephen.
12737:
12731:
12730:
12728:
12726:
12713:
12707:
12706:
12698:
12689:
12688:
12684:
12682:
12681:
12676:
12664:
12662:
12661:
12656:
12628:
12615:
12606:
12605:
12532:
12523:
12512:
12506:
12500:
12498:
12462:
12453:
12452:
12446:
12438:
12430:
12424:
12423:
12421:
12419:
12408:
12402:
12384:
12378:
12377:
12374:Internet Archive
12361:
12348:
12342:
12341:
12309:
12293:
12290:
12268:Residual entropy
12242:Harmonic entropy
12227:Entropy and life
12197:Brownian ratchet
12142:paradigm founder
12098:Ludwig Boltzmann
12082:Jacob Bekenstein
11979:
11977:
11976:
11971:
11959:
11957:
11956:
11951:
11946:
11934:
11932:
11931:
11926:
11921:
11909:
11907:
11906:
11901:
11899:
11894:
11890:
11884:
11876:
11869:
11863:
11857:
11851:
11850:
11849:
11838:
11837:
11833:
11831:
11823:
11815:
11794:
11792:
11791:
11786:
11781:
11770:
11758:
11756:
11755:
11750:
11738:
11736:
11735:
11730:
11710:
11708:
11707:
11702:
11690:
11688:
11687:
11682:
11666:
11664:
11663:
11658:
11656:
11629:
11627:
11626:
11621:
11609:
11607:
11606:
11601:
11599:
11585:
11584:
11583:
11582:
11566:
11565:
11554:
11549:
11514:
11512:
11511:
11506:
11501:
11474:
11472:
11471:
11466:
11442:binary logarithm
11439:
11437:
11436:
11431:
11429:
11428:
11424:
11423:
11398:
11397:
11380:
11375:
11335:
11333:
11332:
11327:
11325:
11324:
11289:
11282:John von Neumann
11233:
11224:
11222:
11221:
11216:
11214:
11213:
11212:
11211:
11195:
11194:
11183:
11174:
11173:
11172:
11146:
11144:
11143:
11138:
11136:
11135:
11104:
11102:
11101:
11096:
11094:
11093:
11092:
11071:
11069:
11068:
11063:
11061:
11042:
11040:
11039:
11034:
11032:
11031:
11023:
11013:
11011:
11010:
11005:
11003:
11002:
10998:
10997:
10996:
10988:
10976:
10975:
10967:
10958:
10948:
10947:
10946:
10945:
10914:John von Neumann
10893:
10891:
10890:
10885:
10883:
10882:
10866:
10864:
10863:
10858:
10834:
10832:
10831:
10826:
10824:
10823:
10807:
10805:
10804:
10799:
10787:
10785:
10784:
10779:
10767:
10765:
10764:
10759:
10747:
10745:
10744:
10739:
10727:
10725:
10724:
10719:
10717:
10716:
10700:
10698:
10697:
10692:
10690:
10689:
10668:J. Yngvason
10572:
10551:Energy dispersal
10546:
10544:
10543:
10538:
10536:
10535:
10534:
10516:channel capacity
10513:
10511:
10510:
10505:
10503:
10502:
10501:
10484:
10482:
10481:
10476:
10474:
10473:
10472:
10455:
10453:
10452:
10447:
10445:
10443:
10442:
10441:
10431:
10430:
10429:
10419:
10408:
10407:
10382:
10380:
10379:
10374:
10372:
10370:
10369:
10368:
10358:
10357:
10356:
10346:
10341:
10340:
10248:energy dispersal
10226:
10224:
10223:
10218:
10216:
10214:
10213:
10212:
10202:
10201:
10200:
10199:
10179:
10174:
10173:
10172:
10142:
10140:
10139:
10134:
10132:
10131:
10130:
10109:
10107:
10106:
10101:
10096:
10094:
10093:
10092:
10082:
10081:
10080:
10079:
10059:
10054:
10053:
10052:
10022:
10020:
10019:
10014:
10012:
10011:
10010:
9977:
9975:
9974:
9969:
9967:
9965:
9964:
9952:
9935:
9933:
9932:
9920:
9912:
9911:
9910:
9881:
9879:
9878:
9873:
9871:
9869:
9868:
9856:
9839:
9837:
9836:
9824:
9816:
9815:
9814:
9771:
9769:
9768:
9763:
9761:
9760:
9759:
9742:
9740:
9739:
9734:
9732:
9730:
9729:
9717:
9709:
9708:
9707:
9674:phase transition
9671:
9669:
9668:
9663:
9661:
9660:
9659:
9635:
9633:
9632:
9627:
9625:
9623:
9622:
9610:
9602:
9601:
9600:
9568:
9566:
9565:
9560:
9548:
9546:
9545:
9540:
9538:
9537:
9505:
9503:
9502:
9497:
9481:
9479:
9478:
9473:
9461:
9459:
9458:
9453:
9451:
9449:
9448:
9436:
9416:
9414:
9413:
9401:
9371:
9369:
9368:
9363:
9351:
9349:
9348:
9343:
9331:
9329:
9328:
9323:
9321:
9320:
9304:
9302:
9301:
9296:
9294:
9293:
9257:
9255:
9254:
9249:
9241:
9240:
9239:
9227:
9226:
9218:
9206:
9204:
9203:
9198:
9196:
9195:
9194:
9182:
9181:
9173:
9159:
9157:
9156:
9151:
9139:
9137:
9136:
9131:
9129:
9128:
9112:
9110:
9109:
9104:
9092:
9090:
9089:
9084:
9082:
9081:
9076:
9075:
9067:
9056:
9054:
9053:
9048:
9046:
9045:
9044:
9035:
9030:
9029:
9024:
9023:
9015:
9009:
8993:
8991:
8990:
8985:
8980:
8975:
8974:
8966:
8933:
8931:
8930:
8925:
8923:
8922:
8921:
8909:
8908:
8900:
8889:
8887:
8886:
8881:
8876:
8871:
8870:
8862:
8852:
8850:
8849:
8844:
8842:
8841:
8836:
8835:
8827:
8816:
8814:
8813:
8808:
8806:
8805:
8800:
8799:
8791:
8780:
8778:
8777:
8772:
8770:
8769:
8768:
8763:
8762:
8754:
8750:
8749:
8744:
8743:
8735:
8729:
8724:
8702:
8700:
8699:
8694:
8692:
8691:
8690:
8689:
8677:
8676:
8668:
8661:
8656:
8648:
8646:
8641:
8640:
8635:
8634:
8626:
8622:
8621:
8616:
8615:
8607:
8601:
8596:
8578:
8576:
8572:
8566:
8562:
8556:
8547:
8545:
8544:
8539:
8527:
8525:
8524:
8519:
8506:
8504:
8503:
8498:
8486:
8484:
8483:
8478:
8466:
8464:
8463:
8458:
8446:
8444:
8443:
8438:
8426:
8424:
8423:
8418:
8413:
8408:
8400:
8384:
8382:
8381:
8376:
8354:is the absolute
8353:
8351:
8350:
8345:
8333:
8331:
8330:
8325:
8320:
8315:
8314:
8306:
8296:
8294:
8293:
8288:
8286:
8285:
8277:
8264:
8262:
8261:
8256:
8254:
8253:
8252:
8246:
8245:
8237:
8226:
8224:
8223:
8218:
8216:
8215:
8207:
8131:A 2011 study in
8116:
8114:
8113:
8108:
8089:
8087:
8086:
8081:
8066:
8064:
8063:
8058:
8048:
8019:
8017:
8016:
8011:
7999:
7997:
7996:
7991:
7972:
7970:
7969:
7964:
7962:
7961:
7960:
7929:
7928:
7927:
7878:
7877:
7876:
7835:
7833:
7832:
7827:
7809:
7805:
7803:
7802:
7797:
7792:
7787:
7786:
7785:
7762:
7758:
7695:
7693:
7692:
7687:
7675:
7673:
7672:
7667:
7662:
7655:
7645:
7638:
7628:
7616:
7614:
7613:
7608:
7596:
7594:
7593:
7588:
7572:
7570:
7569:
7564:
7511:
7509:
7508:
7503:
7501:
7500:
7484:
7482:
7481:
7476:
7471:
7470:
7454:
7452:
7451:
7446:
7441:
7423:
7421:
7420:
7415:
7400:
7398:
7397:
7392:
7357:perpetual motion
7309:
7307:
7306:
7301:
7299:
7295:
7294:
7244:
7242:
7241:
7236:
7234:
7229:
7228:
7227:
7226:
7206:
7198:
7186:
7184:
7183:
7178:
7176:
7175:
7174:
7173:
7157:
7156:
7145:
7136:
7135:
7134:
7056:arrow of entropy
7052:perpetual motion
7048:isolated systems
7008:room temperature
6935:detailed balance
6927:Markov processes
6921:
6919:
6918:
6913:
6901:
6899:
6898:
6893:
6881:
6879:
6878:
6873:
6861:
6859:
6858:
6853:
6841:
6839:
6838:
6833:
6821:
6819:
6818:
6813:
6801:
6799:
6798:
6793:
6781:
6779:
6778:
6773:
6761:
6759:
6758:
6753:
6725:
6723:
6722:
6717:
6715:
6704:
6703:
6702:
6678:
6676:
6675:
6670:
6658:
6656:
6655:
6650:
6645:
6634:
6633:
6604:
6602:
6601:
6596:
6575:matrix logarithm
6572:
6570:
6569:
6564:
6548:
6546:
6545:
6540:
6538:
6519:
6517:
6516:
6511:
6509:
6508:
6500:
6490:
6488:
6487:
6482:
6480:
6479:
6475:
6474:
6473:
6465:
6453:
6452:
6444:
6435:
6425:
6424:
6423:
6422:
6396:
6394:
6393:
6388:
6386:
6382:
6381:
6365:
6364:
6363:
6318:
6316:
6315:
6310:
6308:
6307:
6306:
6289:
6287:
6286:
6281:
6279:
6278:
6277:
6276:
6260:
6259:
6248:
6239:
6238:
6237:
6207:
6205:
6204:
6199:
6197:
6196:
6105:Ludwig Boltzmann
6075:
6073:
6072:
6067:
6046:
6044:
6043:
6038:
6023:
6021:
6020:
6015:
6003:
6001:
6000:
5995:
5965:
5963:
5962:
5959:{\textstyle S=0}
5957:
5940:have an entropy
5916:
5914:
5913:
5908:
5906:
5901:
5900:
5899:
5898:
5878:
5870:
5854:
5852:
5851:
5846:
5833:path-independent
5830:
5828:
5827:
5822:
5820:
5816:
5811:
5810:
5809:
5789:
5788:
5772:
5770:
5769:
5764:
5756:
5751:
5750:
5749:
5748:
5728:
5606:
5605:
5593:
5592:
5569:de Broglie waves
5539:
5537:
5536:
5531:
5523:
5522:
5521:
5499:
5498:
5497:
5471:
5469:
5468:
5463:
5461:
5460:
5453:
5452:
5431:
5429:
5428:
5423:
5415:
5413:
5412:
5411:
5401:
5400:
5399:
5389:
5384:
5382:
5381:
5380:
5370:
5369:
5368:
5358:
5349:
5347:
5346:
5341:
5329:
5327:
5326:
5321:
5319:
5318:
5317:
5307:
5303:
5302:
5300:
5299:
5298:
5288:
5287:
5286:
5276:
5250:
5248:
5247:
5242:
5228:for a cold one.
5227:
5225:
5224:
5219:
5217:
5216:
5203:
5201:
5200:
5195:
5193:
5192:
5179:
5177:
5176:
5171:
5159:
5157:
5156:
5151:
5149:
5148:
5139:
5134:
5133:
5118:
5117:
5110:
5109:
5088:
5086:
5085:
5080:
5072:
5071:
5070:
5048:
5047:
5046:
5024:
5022:
5021:
5020:
5010:
5009:
5008:
4998:
4993:
4991:
4990:
4989:
4979:
4978:
4977:
4967:
4947:
4945:
4944:
4939:
4934:
4917:
4905:
4903:
4902:
4897:
4882:
4880:
4879:
4874:
4866:
4864:
4863:
4862:
4852:
4851:
4850:
4840:
4835:
4833:
4832:
4831:
4821:
4820:
4819:
4809:
4804:
4802:
4801:
4800:
4790:
4786:
4785:
4784:
4770:
4765:
4763:
4762:
4761:
4751:
4747:
4746:
4745:
4731:
4711:
4709:
4708:
4703:
4698:
4678:
4666:
4664:
4663:
4658:
4642:
4640:
4639:
4634:
4626:
4625:
4624:
4611:
4610:
4609:
4590:
4586:
4585:
4584:
4567:
4563:
4562:
4561:
4538:
4537:
4515:
4513:
4512:
4507:
4489:
4487:
4486:
4481:
4463:
4461:
4460:
4455:
4443:
4441:
4440:
4435:
4433:
4429:
4428:
4427:
4410:
4406:
4405:
4404:
4387:
4386:
4370:
4368:
4367:
4362:
4336:
4334:
4333:
4328:
4326:
4325:
4324:
4314:
4310:
4309:
4307:
4306:
4305:
4295:
4294:
4293:
4283:
4267:
4266:
4265:
4252:
4250:
4249:
4248:
4238:
4237:
4236:
4235:
4222:
4221:
4220:
4209:
4194:
4192:
4191:
4186:
4184:
4183:
4182:
4165:
4163:
4162:
4157:
4137:
4135:
4134:
4129:
4127:
4126:
4125:
4108:
4106:
4105:
4100:
4098:
4097:
4096:
4076:, as he assumed
4075:
4073:
4072:
4067:
4065:
4064:
4063:
4046:
4044:
4043:
4038:
4036:
4035:
4034:
4017:
4015:
4014:
4009:
3993:Carnot's theorem
3986:
3984:
3983:
3978:
3976:
3975:
3974:
3957:
3955:
3954:
3949:
3947:
3946:
3945:
3924:
3922:
3921:
3916:
3914:
3913:
3912:
3895:
3893:
3892:
3887:
3885:
3884:
3883:
3859:'s study of the
3834:
3832:
3831:
3826:
3824:
3819:
3818:
3817:
3816:
3796:
3788:
3771:
3769:
3768:
3763:
3746:
3744:
3743:
3738:
3736:
3735:
3734:
3703:
3701:
3700:
3695:
3690:
3609:
3559:
3558:
3551:
3550:
3533:
3527:
3521:
3456:Ludwig Boltzmann
3442:
3428:
3427:
3409:chemical species
3398:
3260:Ludwig Boltzmann
3140:
3133:
3126:
3017:Systems thinking
2943:Self-replication
2881:Machine learning
2835:Dynamic networks
2756:Phase transition
2695:
2694:
2685:
2678:
2671:
2336:SkĆodowska-Curie
2218:Condensed matter
2183:Weak interaction
2178:Electromagnetism
2035:Louis de Broglie
1963:
1961:
1960:
1955:
1953:
1952:
1940:
1932:
1931:
1913:
1912:
1893:
1891:
1890:
1885:
1871:
1870:
1861:
1856:
1854:
1843:
1820:
1819:
1810:
1805:
1804:
1796:
1778:
1777:
1768:
1761:
1754:
1716:Entropy articles
1712:
1711:
1702:
1695:
1688:
1672:
1671:
1379:Key publications
1360:
1359:("living force")
1309:Brownian ratchet
1304:Entropy and life
1299:Entropy and time
1250:
1249:
1225:
1223:
1222:
1217:
1170:
1168:
1167:
1162:
1115:
1113:
1112:
1107:
1060:
1058:
1057:
1052:
954:Clausius theorem
949:Carnot's theorem
922:
920:
919:
914:
898:
896:
895:
890:
875:
873:
872:
867:
851:
849:
848:
843:
830:
829:
826:
824:
823:
818:
790:
788:
787:
782:
766:
764:
763:
758:
743:
741:
740:
735:
719:
717:
716:
711:
698:
697:
694:
692:
691:
686:
655:
653:
652:
647:
631:
629:
628:
623:
608:
606:
605:
600:
584:
582:
581:
576:
563:
562:
559:
557:
556:
551:
529:
528:
402:
401:
221:
220:
102:
88:
87:
78:
44:
43:
39:
32:
25:
18506:
18505:
18501:
18500:
18499:
18497:
18496:
18495:
18481:State functions
18456:
18455:
18454:
18449:
18415:System dynamics
18376:
18362:Spatial ecology
18323:
18265:
18251:Systems biology
18202:
18169:
18140:Artificial life
18110:
18101:
18097:Swarm behaviour
18082:Synchronization
18042:Social dynamics
18033:
18026:
18005:
18003:Complex systems
18000:
17970:
17965:
17910:
17872:
17837:
17819:BBGKY hierarchy
17814:Vlasov equation
17792:
17781:depletion force
17774:Particles with
17734:
17673:
17669:
17664:
17643:
17638:
17608:
17603:
17547:
17543:Waste-to-energy
17521:
17457:Energy security
17403:
17397:
17253:
17245:
17224:Natural uranium
17158:
17139:Mechanical wave
17070:Energy carriers
17064:
16904:
16833:Isolated system
16711:
16705:
16682:
16677:
16594:More on Entropy
16556:
16551:
16545:
16493:
16492:
16488:
16467:
16448:
16440:. McGraw-Hill.
16427:
16403:
16376:
16366:Thermal Physics
16357:
16336:
16313:
16294:
16271:
16249:
16221:
16220:
16216:
16193:
16161:
16160:
16156:
16137:
16115:
16103:Thermal Physics
16092:
16073:
16057:Adam, Gerhard;
16052:
16050:Further reading
16039:
16037:
16020:
16010:
16008:
15970:Daly, Herman E.
15967:
15963:
15925:
15919:
15915:
15877:
15868:
15864:
15857:
15846:
15838:
15834:
15827:
15816:
15808:Daly, Herman E.
15805:
15801:
15763:
15759:
15749:
15747:
15719:Barrow, John D.
15714:
15705:
15701:
15694:
15680:
15676:
15669:
15655:
15651:
15644:
15630:
15626:
15619:
15603:
15599:
15588:
15584:
15574:
15572:
15570:
15552:
15548:
15488:
15484:
15431:Phys. Rev. Lett
15427:
15423:
15407:
15406:
15402:
15386:
15382:
15343:
15339:
15286:
15282:
15247:
15243:
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15142:
15141:
15137:
15123:
15119:
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15098:
15094:
15081:
15080:
15076:
15069:
15047:
15043:
15000:
14996:
14991:
14987:
14967:
14965:
14963:
14945:
14941:
14934:
14916:
14912:
14881:
14877:
14870:
14856:
14852:
14845:
14829:
14822:
14815:
14801:
14797:
14790:
14776:
14772:
14745:
14741:
14734:
14718:
14714:
14679:
14675:
14630:Physics Reports
14626:
14622:
14615:
14601:Wise, M. Norton
14597:
14593:
14578:
14574:
14567:
14551:
14547:
14504:
14500:
14476:
14470:
14466:
14455:
14451:
14424:Physics Letters
14420:
14413:
14374:
14367:
14360:
14346:
14337:
14327:
14325:
14317:
14316:
14312:
14305:
14289:
14285:
14275:
14273:
14271:
14253:
14249:
14239:
14237:
14232:
14231:
14227:
14222:on 9 July 2017.
14219:
14212:
14206:
14202:
14192:
14190:
14181:
14180:
14176:
14160:
14159:
14155:
14141:
14137:
14118:
14111:
14104:
14090:
14086:
14079:
14063:
14059:
14012:(6025): 60â65.
13998:
13991:
13984:
13976:. McGraw-Hill.
13966:
13962:
13923:
13919:
13912:
13904:. Brooks Cole.
13894:
13887:
13834:
13830:
13819:
13815:
13778:
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13313:
13309:
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13255:
13248:
13238:
13236:
13232:
13224:
13220:
13177:
13173:
13166:
13144:
13140:
13130:Wayback Machine
13121:
13114:
13107:
13093:
13089:
13082:
13060:
13053:
13046:
13032:
13023:
13016:
13002:
12998:
12991:
12977:
12973:
12958:
12954:
12947:
12931:
12927:
12912:
12905:
12898:
12884:
12880:
12873:
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12847:
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12793:
12789:
12779:
12777:
12765:
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12760:
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12748:
12738:
12734:
12724:
12722:
12715:
12714:
12710:
12699:
12692:
12670:
12667:
12666:
12650:
12647:
12646:
12641:
12616:
12609:
12563:. p. 390:
12533:
12526:
12513:
12509:
12463:
12456:
12440:
12439:
12431:
12427:
12417:
12415:
12410:
12409:
12405:
12385:
12381:
12370:
12349:
12345:
12310:
12306:
12302:
12297:
12296:
12291:
12287:
12282:
12277:
12187:
12150:magnum opus on
12127:
12117:
12086:Stephen Hawking
12050:
12034:
12026:isolated system
12018:
12002:thermoeconomics
11990:
11965:
11962:
11961:
11942:
11940:
11937:
11936:
11917:
11915:
11912:
11911:
11886:
11885:
11883:
11872:
11839:
11824:
11816:
11814:
11810:
11809:
11808:
11800:
11797:
11796:
11777:
11766:
11764:
11761:
11760:
11744:
11741:
11740:
11724:
11721:
11720:
11717:
11696:
11693:
11692:
11676:
11673:
11672:
11652:
11635:
11632:
11631:
11615:
11612:
11611:
11595:
11578:
11574:
11573:
11561:
11557:
11556:
11550:
11539:
11524:
11521:
11520:
11497:
11486:
11483:
11482:
11460:
11457:
11456:
11444:corresponds to
11419:
11415:
11408:
11393:
11389:
11382:
11376:
11365:
11341:
11338:
11337:
11320:
11316:
11314:
11311:
11310:
11303:Shannon entropy
11291:
11275:
11266:
11254:Main articles:
11252:
11207:
11203:
11202:
11190:
11186:
11185:
11179:
11168:
11167:
11163:
11152:
11149:
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11131:
11127:
11125:
11122:
11121:
11118:classical limit
11088:
11087:
11083:
11081:
11078:
11077:
11054:
11052:
11049:
11048:
11022:
11021:
11019:
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10987:
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10960:
10959:
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10941:
10940:
10936:
10925:
10922:
10921:
10906:
10900:
10878:
10874:
10872:
10869:
10868:
10867:, in the state
10840:
10837:
10836:
10819:
10815:
10813:
10810:
10809:
10793:
10790:
10789:
10773:
10770:
10769:
10753:
10750:
10749:
10733:
10730:
10729:
10712:
10708:
10706:
10703:
10702:
10685:
10681:
10679:
10676:
10675:
10656:
10632:
10608:isolated system
10561:
10559:
10553:
10530:
10529:
10525:
10523:
10520:
10519:
10497:
10496:
10492:
10490:
10487:
10486:
10468:
10467:
10463:
10461:
10458:
10457:
10437:
10436:
10432:
10425:
10424:
10420:
10418:
10391:
10390:
10388:
10385:
10384:
10364:
10363:
10359:
10352:
10351:
10347:
10345:
10315:
10314:
10312:
10309:
10308:
10280:
10274:
10240:
10232:
10208:
10207:
10203:
10189:
10188:
10184:
10180:
10178:
10162:
10161:
10157:
10152:
10149:
10148:
10126:
10125:
10121:
10119:
10116:
10115:
10110:Similarly, for
10088:
10087:
10083:
10069:
10068:
10064:
10060:
10058:
10042:
10041:
10037:
10032:
10029:
10028:
10006:
10005:
10001:
9999:
9996:
9995:
9983:
9960:
9956:
9951:
9928:
9924:
9919:
9906:
9905:
9901:
9887:
9884:
9883:
9864:
9860:
9855:
9832:
9828:
9823:
9810:
9809:
9805:
9791:
9788:
9787:
9755:
9754:
9750:
9748:
9745:
9744:
9725:
9721:
9716:
9703:
9702:
9698:
9684:
9681:
9680:
9655:
9654:
9650:
9648:
9645:
9644:
9618:
9614:
9609:
9596:
9595:
9591:
9577:
9574:
9573:
9554:
9551:
9550:
9533:
9529:
9527:
9524:
9523:
9520:
9491:
9488:
9487:
9467:
9464:
9463:
9444:
9440:
9435:
9409:
9405:
9400:
9377:
9374:
9373:
9357:
9354:
9353:
9337:
9334:
9333:
9316:
9312:
9310:
9307:
9306:
9289:
9285:
9283:
9280:
9279:
9272:
9264:
9229:
9228:
9217:
9216:
9215:
9213:
9210:
9209:
9184:
9183:
9172:
9171:
9170:
9168:
9165:
9164:
9145:
9142:
9141:
9124:
9120:
9118:
9115:
9114:
9098:
9095:
9094:
9077:
9066:
9065:
9064:
9062:
9059:
9058:
9040:
9036:
9031:
9025:
9014:
9013:
9012:
9011:
9005:
8999:
8996:
8995:
8994:is replaced by
8976:
8965:
8964:
8962:
8959:
8958:
8934:is the rate of
8911:
8910:
8899:
8898:
8897:
8895:
8892:
8891:
8872:
8861:
8860:
8858:
8855:
8854:
8837:
8826:
8825:
8824:
8822:
8819:
8818:
8801:
8790:
8789:
8788:
8786:
8783:
8782:
8764:
8753:
8752:
8751:
8745:
8734:
8733:
8732:
8731:
8725:
8714:
8708:
8705:
8704:
8679:
8678:
8667:
8666:
8665:
8647:
8645:
8636:
8625:
8624:
8623:
8617:
8606:
8605:
8604:
8603:
8597:
8586:
8568:
8567:
8558:
8557:
8555:
8553:
8550:
8549:
8533:
8530:
8529:
8513:
8510:
8509:
8492:
8489:
8488:
8472:
8469:
8468:
8452:
8449:
8448:
8432:
8429:
8428:
8409:
8404:
8396:
8394:
8391:
8390:
8370:
8367:
8366:
8339:
8336:
8335:
8316:
8305:
8304:
8302:
8299:
8298:
8276:
8275:
8270:
8267:
8266:
8248:
8247:
8236:
8235:
8234:
8232:
8229:
8228:
8206:
8205:
8203:
8200:
8199:
8168:
8129:
8123:
8099:
8096:
8095:
8072:
8069:
8068:
8025:
8022:
8021:
8005:
8002:
8001:
7982:
7979:
7978:
7941:
7940:
7936:
7890:
7889:
7885:
7851:
7850:
7846:
7841:
7838:
7837:
7818:
7815:
7814:
7807:
7788:
7775:
7774:
7770:
7768:
7765:
7764:
7760:
7756:
7725:isolated system
7713:
7681:
7678:
7677:
7658:
7641:
7624:
7622:
7619:
7618:
7602:
7599:
7598:
7582:
7579:
7578:
7558:
7555:
7554:
7550:
7544:
7539:
7496:
7492:
7490:
7487:
7486:
7466:
7462:
7460:
7457:
7456:
7437:
7429:
7426:
7425:
7406:
7403:
7402:
7386:
7383:
7382:
7368:air conditioner
7340:
7335:
7290:
7286:
7282:
7274:
7271:
7270:
7216:
7215:
7211:
7207:
7205:
7194:
7192:
7189:
7188:
7169:
7165:
7164:
7152:
7148:
7147:
7141:
7130:
7129:
7125:
7114:
7111:
7110:
7103:
7079:isolated system
7023:entropy of the
7020:isolated system
6995:(more possible
6950:
6907:
6904:
6903:
6887:
6884:
6883:
6867:
6864:
6863:
6847:
6844:
6843:
6827:
6824:
6823:
6807:
6804:
6803:
6787:
6784:
6783:
6767:
6764:
6763:
6747:
6744:
6743:
6711:
6698:
6697:
6693:
6685:
6682:
6681:
6664:
6661:
6660:
6641:
6629:
6625:
6623:
6620:
6619:
6590:
6587:
6586:
6558:
6555:
6554:
6531:
6529:
6526:
6525:
6499:
6498:
6496:
6493:
6492:
6464:
6463:
6443:
6442:
6441:
6437:
6436:
6428:
6418:
6417:
6413:
6402:
6399:
6398:
6377:
6370:
6366:
6359:
6358:
6354:
6343:
6340:
6339:
6302:
6301:
6297:
6295:
6292:
6291:
6272:
6268:
6267:
6255:
6251:
6250:
6244:
6233:
6232:
6228:
6217:
6214:
6213:
6192:
6188:
6186:
6183:
6182:
6101:
6095:
6052:
6049:
6048:
6029:
6026:
6025:
6009:
6006:
6005:
5986:
5983:
5982:
5945:
5942:
5941:
5888:
5887:
5883:
5879:
5877:
5866:
5864:
5861:
5860:
5840:
5837:
5836:
5812:
5799:
5798:
5794:
5790:
5784:
5780:
5778:
5775:
5774:
5738:
5737:
5733:
5729:
5727:
5722:
5719:
5718:
5672:isolated system
5668:Rudolf Clausius
5655:Particle number
5598:
5591:
5585:
5511:
5510:
5506:
5487:
5486:
5482:
5477:
5474:
5473:
5448:
5447:
5446:
5442:
5437:
5434:
5433:
5407:
5406:
5402:
5395:
5394:
5390:
5388:
5376:
5375:
5371:
5364:
5363:
5359:
5357:
5355:
5352:
5351:
5335:
5332:
5331:
5313:
5312:
5308:
5294:
5293:
5289:
5282:
5281:
5277:
5275:
5268:
5264:
5256:
5253:
5252:
5236:
5233:
5232:
5212:
5211:
5209:
5206:
5205:
5188:
5187:
5185:
5182:
5181:
5165:
5162:
5161:
5144:
5140:
5135:
5129:
5125:
5105:
5104:
5103:
5099:
5094:
5091:
5090:
5060:
5059:
5055:
5036:
5035:
5031:
5016:
5015:
5011:
5004:
5003:
4999:
4997:
4985:
4984:
4980:
4973:
4972:
4968:
4966:
4961:
4958:
4957:
4930:
4913:
4911:
4908:
4907:
4891:
4888:
4887:
4858:
4857:
4853:
4846:
4845:
4841:
4839:
4827:
4826:
4822:
4815:
4814:
4810:
4808:
4796:
4795:
4791:
4780:
4779:
4775:
4771:
4769:
4757:
4756:
4752:
4741:
4740:
4736:
4732:
4730:
4728:
4725:
4724:
4714:internal energy
4694:
4674:
4672:
4669:
4668:
4652:
4649:
4648:
4620:
4619:
4615:
4605:
4604:
4600:
4580:
4579:
4575:
4571:
4557:
4556:
4552:
4548:
4533:
4529:
4521:
4518:
4517:
4495:
4492:
4491:
4469:
4466:
4465:
4449:
4446:
4445:
4423:
4422:
4418:
4414:
4400:
4399:
4395:
4391:
4382:
4378:
4376:
4373:
4372:
4350:
4347:
4346:
4320:
4319:
4315:
4301:
4300:
4296:
4289:
4288:
4284:
4282:
4275:
4271:
4261:
4260:
4256:
4244:
4243:
4239:
4231:
4230:
4226:
4216:
4215:
4211:
4210:
4208:
4200:
4197:
4196:
4178:
4177:
4173:
4171:
4168:
4167:
4151:
4148:
4147:
4121:
4120:
4116:
4114:
4111:
4110:
4092:
4091:
4087:
4085:
4082:
4081:
4059:
4058:
4054:
4052:
4049:
4048:
4030:
4029:
4025:
4023:
4020:
4019:
4003:
4000:
3999:
3970:
3969:
3965:
3963:
3960:
3959:
3941:
3940:
3936:
3934:
3931:
3930:
3908:
3907:
3903:
3901:
3898:
3897:
3879:
3878:
3874:
3872:
3869:
3868:
3857:Rudolf Clausius
3853:
3806:
3805:
3801:
3797:
3795:
3784:
3782:
3779:
3778:
3757:
3754:
3753:
3724:
3723:
3719:
3714:
3711:
3710:
3686:
3684:
3681:
3680:
3676:
3647:state functions
3643:state variables
3631:
3611:
3601:
3592:
3508:
3389:resulting in a
3386:Rudolf Clausius
3310:
3300:Rudolf Clausius
3293:
3237:Rudolf Clausius
3225:William Rankine
3191:weather science
3144:
3115:
3114:
3113:
3108:
3104:
3099:
3094:
3084:
3083:
3078:
3074:
3070:
3066:
3062:
3058:
3054:
3049:
3044:
3034:
3033:
3032:
3027:
3023:
3019:
3015:
3013:Systems science
3011:
3009:System dynamics
3007:
3003:
2999:
2995:
2991:
2987:
2983:
2979:
2975:
2970:
2965:
2951:
2950:
2945:
2941:
2939:Spatial ecology
2937:
2933:
2929:
2925:
2921:
2916:
2911:
2901:
2900:
2895:
2891:
2887:
2883:
2879:
2877:Artificial life
2875:
2871:
2867:
2862:
2857:
2843:
2842:
2837:
2833:
2831:Systems biology
2829:
2825:
2821:
2817:
2813:
2809:
2805:
2800:
2795:
2785:
2784:
2783:
2778:
2776:Swarm behaviour
2774:
2770:
2766:
2764:Synchronization
2762:
2758:
2754:
2750:
2746:
2742:
2737:
2735:Social dynamics
2732:
2722:
2721:
2720:
2715:
2699:Complex systems
2689:
2660:
2659:
2656:
2655:
2654:
2644:
2636:
2635:
2296:
2288:
2287:
2278:Quantum gravity
2228:Complex systems
2126:
2118:
2117:
2053:
2045:
2044:
1990:Albert Einstein
1980:
1972:
1945:
1941:
1936:
1924:
1920:
1905:
1901:
1899:
1896:
1895:
1894:
1866:
1862:
1857:
1847:
1842:
1815:
1811:
1806:
1795:
1794:
1792:
1789:
1788:
1772:
1706:
1661:
1660:
1636:
1628:
1627:
1626:
1486:
1478:
1477:
1456:
1442:
1417:
1413:
1406:
1402:
1395:
1391:
1358:
1351:
1333:
1314:Maxwell's demon
1276:
1247:
1246:
1230:
1229:
1228:
1181:
1178:
1177:
1176:
1126:
1123:
1122:
1121:
1071:
1068:
1067:
1066:
1031:
1028:
1027:
1026:
1024:Internal energy
1019:
1004:
994:
993:
968:
943:
933:
932:
931:
905:
902:
901:
884:
881:
880:
858:
855:
854:
837:
834:
833:
809:
806:
805:
773:
770:
769:
752:
749:
748:
726:
723:
722:
705:
702:
701:
674:
671:
670:
665:Compressibility
638:
635:
634:
617:
614:
613:
591:
588:
587:
570:
567:
566:
542:
539:
538:
518:
508:
507:
488:Particle number
441:
400:
389:
379:
378:
337:Irreversibility
249:State of matter
216:Isolated system
201:
191:
190:
189:
164:
154:
153:
149:Non-equilibrium
141:
116:
108:
76:
54:
40:
33:
26:
19:
17:
12:
11:
5:
18504:
18494:
18493:
18488:
18483:
18478:
18473:
18468:
18451:
18450:
18448:
18447:
18442:
18437:
18432:
18427:
18422:
18417:
18412:
18407:
18405:Self-reference
18402:
18397:
18392:
18386:
18384:
18382:Systems theory
18378:
18377:
18375:
18374:
18369:
18364:
18359:
18354:
18349:
18344:
18339:
18333:
18331:
18325:
18324:
18322:
18321:
18316:
18311:
18309:Multistability
18306:
18301:
18296:
18291:
18286:
18281:
18275:
18273:
18267:
18266:
18264:
18263:
18258:
18253:
18248:
18243:
18238:
18233:
18228:
18223:
18218:
18212:
18210:
18204:
18203:
18201:
18200:
18195:
18190:
18185:
18179:
18177:
18171:
18170:
18168:
18167:
18162:
18157:
18152:
18147:
18142:
18137:
18132:
18127:
18122:
18116:
18114:
18103:
18102:
18100:
18099:
18094:
18089:
18084:
18079:
18074:
18069:
18067:Herd mentality
18064:
18059:
18054:
18049:
18044:
18038:
18036:
18028:
18027:
18025:
18024:
18019:
18013:
18011:
18007:
18006:
17999:
17998:
17991:
17984:
17976:
17967:
17966:
17964:
17963:
17962:
17961:
17956:
17951:
17944:Complex system
17941:
17936:
17935:
17934:
17929:
17918:
17916:
17912:
17911:
17909:
17908:
17903:
17898:
17893:
17888:
17882:
17880:
17874:
17873:
17871:
17870:
17869:
17868:
17863:
17853:
17847:
17845:
17839:
17838:
17836:
17835:
17826:
17821:
17816:
17811:
17806:
17800:
17798:
17794:
17793:
17791:
17790:
17789:
17788:
17783:
17772:
17771:
17770:
17765:
17760:
17755:
17744:
17742:
17736:
17735:
17733:
17732:
17727:
17726:
17725:
17720:
17715:
17710:
17699:
17694:
17689:
17683:
17681:
17675:
17674:
17667:
17665:
17663:
17662:
17660:ergodic theory
17657:
17651:
17649:
17645:
17644:
17637:
17636:
17629:
17622:
17614:
17605:
17604:
17602:
17601:
17589:
17577:
17565:
17552:
17549:
17548:
17546:
17545:
17540:
17538:Jevons paradox
17535:
17529:
17527:
17523:
17522:
17520:
17519:
17514:
17509:
17504:
17499:
17494:
17489:
17484:
17479:
17474:
17469:
17464:
17462:Energy storage
17459:
17454:
17453:
17452:
17442:
17437:
17432:
17431:
17430:
17425:
17420:
17409:
17407:
17399:
17398:
17396:
17395:
17394:
17393:
17388:
17378:
17377:
17376:
17371:
17361:
17360:
17359:
17354:
17344:
17339:
17338:
17337:
17332:
17322:
17321:
17320:
17315:
17310:
17300:
17295:
17294:
17293:
17288:
17278:
17273:
17268:
17266:Electric power
17263:
17257:
17255:
17247:
17246:
17244:
17243:
17238:
17233:
17228:
17227:
17226:
17216:
17211:
17206:
17201:
17196:
17195:
17194:
17189:
17184:
17174:
17168:
17166:
17164:Primary energy
17160:
17159:
17157:
17156:
17151:
17146:
17141:
17136:
17135:
17134:
17124:
17123:
17122:
17112:
17111:
17110:
17105:
17095:
17090:
17085:
17080:
17074:
17072:
17066:
17065:
17063:
17062:
17057:
17052:
17047:
17042:
17037:
17032:
17027:
17022:
17017:
17012:
17007:
17002:
16997:
16992:
16987:
16982:
16977:
16972:
16967:
16962:
16961:
16960:
16950:
16945:
16940:
16935:
16930:
16925:
16924:
16923:
16912:
16910:
16906:
16905:
16903:
16902:
16901:
16900:
16895:
16890:
16885:
16880:
16875:
16870:
16865:
16860:
16855:
16850:
16845:
16840:
16835:
16830:
16825:
16820:
16815:
16810:
16805:
16800:
16798:Entropic force
16795:
16788:Thermodynamics
16785:
16780:
16779:
16778:
16773:
16763:
16758:
16753:
16748:
16743:
16738:
16737:
16736:
16726:
16721:
16715:
16713:
16707:
16706:
16704:
16703:
16698:
16693:
16687:
16684:
16683:
16676:
16675:
16668:
16661:
16653:
16647:
16646:
16640:
16634:
16613:
16612:
16611:
16606:
16601:
16596:
16591:
16580:
16574:
16568:
16555:
16554:External links
16552:
16550:
16549:
16543:
16528:
16521:
16518:978-3030354596
16506:
16486:
16471:
16465:
16452:
16446:
16431:
16425:
16411:Penrose, Roger
16407:
16401:
16385:
16380:
16374:
16361:
16355:
16340:
16334:
16317:
16311:
16298:
16292:
16275:
16269:
16261:Thermodynamics
16253:
16247:
16234:
16214:
16197:
16191:
16174:
16154:
16141:
16135:
16119:
16113:
16096:
16090:
16077:
16071:
16053:
16051:
16048:
16047:
16046:
16036:on 27 May 2022
16019:
16018:
15961:
15913:
15862:
15855:
15832:
15825:
15799:
15757:
15699:
15692:
15674:
15667:
15649:
15642:
15624:
15617:
15597:
15582:
15569:978-0470190401
15568:
15546:
15482:
15444:hep-th/9303048
15437:(5): 666â669.
15421:
15400:
15380:
15337:
15280:
15241:
15234:
15206:
15156:
15135:
15117:
15110:
15092:
15074:
15067:
15041:
15014:(1): 286â296.
14994:
14985:
14962:978-3642401534
14961:
14939:
14932:
14910:
14891:(7): 632â636.
14875:
14868:
14850:
14843:
14820:
14813:
14795:
14788:
14770:
14759:(3): 178â184.
14739:
14732:
14712:
14693:(3): 355â386.
14673:
14620:
14613:
14591:
14572:
14565:
14545:
14498:
14464:
14449:
14430:(4): 171â173.
14411:
14365:
14358:
14335:
14310:
14303:
14283:
14270:978-1489983671
14269:
14247:
14234:"GRC.nasa.gov"
14225:
14200:
14183:"GRC.nasa.gov"
14174:
14153:
14135:
14109:
14102:
14094:Thermodynamics
14084:
14077:
14057:
13989:
13982:
13960:
13917:
13910:
13885:
13828:
13813:
13772:
13743:
13690:
13629:
13622:
13604:
13545:
13484:
13477:
13459:
13438:(3): 132â136.
13415:
13388:
13381:
13361:
13354:
13336:
13329:
13307:
13300:
13282:
13275:
13246:
13218:
13191:(5): 391â398.
13171:
13164:
13138:
13112:
13105:
13087:
13080:
13051:
13044:
13021:
13014:
12996:
12989:
12971:
12962:Thermodynamics
12952:
12945:
12925:
12903:
12896:
12888:Theory of heat
12878:
12871:
12845:
12838:
12812:
12805:
12787:
12758:
12732:
12708:
12690:
12674:
12654:
12639:
12607:
12565:Sucht man fĂŒr
12547:(7): 353â400.
12524:
12507:
12473:(3): 368â397.
12454:
12425:
12403:
12401:, pp. 576â577.
12379:
12368:
12343:
12324:(2): 221â260.
12303:
12301:
12298:
12295:
12294:
12284:
12283:
12281:
12278:
12276:
12275:
12270:
12265:
12260:
12255:
12249:
12244:
12239:
12234:
12229:
12224:
12219:
12217:Entropic force
12214:
12209:
12204:
12199:
12194:
12188:
12186:
12183:
12116:
12113:
12089:activity (see
12049:
12046:
12033:
12030:
12017:
12014:
11998:psychodynamics
11989:
11986:
11973:{\textstyle T}
11969:
11949:
11945:
11924:
11920:
11897:
11893:
11889:
11882:
11879:
11875:
11868:
11862:
11856:
11848:
11845:
11842:
11836:
11830:
11827:
11822:
11819:
11813:
11807:
11804:
11784:
11780:
11776:
11773:
11769:
11752:{\textstyle V}
11748:
11732:{\textstyle N}
11728:
11716:
11713:
11704:{\textstyle H}
11700:
11684:{\textstyle k}
11680:
11655:
11651:
11648:
11645:
11642:
11639:
11623:{\textstyle k}
11619:
11598:
11594:
11591:
11588:
11581:
11577:
11572:
11569:
11564:
11560:
11553:
11548:
11545:
11542:
11538:
11534:
11531:
11528:
11504:
11500:
11496:
11493:
11490:
11468:{\textstyle W}
11464:
11427:
11422:
11418:
11414:
11411:
11407:
11404:
11401:
11396:
11392:
11388:
11385:
11379:
11374:
11371:
11368:
11364:
11360:
11357:
11354:
11351:
11348:
11345:
11323:
11319:
11307:Claude Shannon
11278:Claude Shannon
11267:
11251:
11248:
11244:density matrix
11210:
11206:
11201:
11198:
11193:
11189:
11182:
11178:
11171:
11166:
11162:
11159:
11156:
11134:
11130:
11091:
11086:
11074:trace operator
11060:
11057:
11045:density matrix
11029:
11026:
11001:
10994:
10991:
10985:
10982:
10979:
10973:
10970:
10963:
10957:
10954:
10944:
10939:
10935:
10932:
10929:
10902:Main article:
10899:
10896:
10881:
10877:
10856:
10853:
10850:
10847:
10844:
10822:
10818:
10797:
10781:{\textstyle X}
10777:
10757:
10741:{\textstyle X}
10737:
10715:
10711:
10688:
10684:
10655:
10652:
10631:
10625:
10589:quantum theory
10555:Main article:
10552:
10549:
10533:
10528:
10500:
10495:
10471:
10466:
10440:
10435:
10428:
10423:
10417:
10414:
10411:
10406:
10403:
10400:
10397:
10394:
10367:
10362:
10355:
10350:
10344:
10339:
10336:
10333:
10330:
10327:
10324:
10321:
10318:
10300:thermodynamics
10276:Main article:
10273:
10270:
10266:
10265:
10258:thermal energy
10254:
10251:
10239:
10236:
10231:
10228:
10211:
10206:
10198:
10195:
10192:
10187:
10183:
10177:
10171:
10168:
10165:
10160:
10156:
10129:
10124:
10099:
10091:
10086:
10078:
10075:
10072:
10067:
10063:
10057:
10051:
10048:
10045:
10040:
10036:
10009:
10004:
9982:
9979:
9963:
9959:
9955:
9950:
9947:
9944:
9941:
9938:
9931:
9927:
9923:
9918:
9915:
9909:
9904:
9900:
9897:
9894:
9891:
9867:
9863:
9859:
9854:
9851:
9848:
9845:
9842:
9835:
9831:
9827:
9822:
9819:
9813:
9808:
9804:
9801:
9798:
9795:
9784:state function
9758:
9753:
9728:
9724:
9720:
9715:
9712:
9706:
9701:
9697:
9694:
9691:
9688:
9658:
9653:
9637:
9636:
9621:
9617:
9613:
9608:
9605:
9599:
9594:
9590:
9587:
9584:
9581:
9562:{\textstyle T}
9558:
9536:
9532:
9519:
9516:
9499:{\textstyle R}
9495:
9475:{\textstyle n}
9471:
9447:
9443:
9439:
9434:
9431:
9428:
9425:
9422:
9419:
9412:
9408:
9404:
9399:
9396:
9393:
9390:
9387:
9384:
9381:
9365:{\textstyle P}
9361:
9345:{\textstyle V}
9341:
9319:
9315:
9292:
9288:
9271:
9268:
9263:
9260:
9247:
9244:
9238:
9235:
9232:
9224:
9221:
9193:
9190:
9187:
9179:
9176:
9153:{\textstyle j}
9149:
9127:
9123:
9106:{\textstyle j}
9102:
9080:
9073:
9070:
9043:
9039:
9034:
9028:
9021:
9018:
9008:
9004:
8983:
8979:
8972:
8969:
8920:
8917:
8914:
8906:
8903:
8879:
8875:
8868:
8865:
8840:
8833:
8830:
8804:
8797:
8794:
8767:
8760:
8757:
8748:
8741:
8738:
8728:
8723:
8720:
8717:
8713:
8688:
8685:
8682:
8674:
8671:
8664:
8659:
8654:
8651:
8644:
8639:
8632:
8629:
8620:
8613:
8610:
8600:
8595:
8592:
8589:
8585:
8581:
8575:
8571:
8565:
8561:
8541:{\textstyle S}
8537:
8521:{\textstyle t}
8517:
8496:
8476:
8456:
8436:
8416:
8412:
8407:
8403:
8399:
8374:
8347:{\textstyle T}
8343:
8323:
8319:
8312:
8309:
8283:
8280:
8274:
8251:
8243:
8240:
8213:
8210:
8167:
8164:
8122:
8119:
8106:
8103:
8079:
8076:
8056:
8053:
8047:
8044:
8041:
8038:
8035:
8032:
8029:
8013:{\textstyle T}
8009:
7989:
7986:
7959:
7956:
7953:
7950:
7947:
7944:
7939:
7935:
7932:
7926:
7923:
7920:
7917:
7914:
7911:
7908:
7905:
7902:
7899:
7896:
7893:
7888:
7884:
7881:
7875:
7872:
7869:
7866:
7863:
7860:
7857:
7854:
7849:
7845:
7825:
7822:
7795:
7791:
7784:
7781:
7778:
7773:
7712:
7709:
7689:{\textstyle T}
7685:
7665:
7661:
7654:
7651:
7648:
7644:
7637:
7634:
7631:
7627:
7610:{\textstyle V}
7606:
7590:{\textstyle p}
7586:
7566:{\textstyle U}
7562:
7546:Main article:
7543:
7540:
7538:
7535:
7499:
7495:
7474:
7469:
7465:
7444:
7440:
7436:
7433:
7413:
7410:
7394:{\textstyle T}
7390:
7353:adiabatic work
7339:
7336:
7334:
7333:
7330:
7327:
7323:
7298:
7293:
7289:
7285:
7281:
7278:
7232:
7225:
7222:
7219:
7214:
7210:
7204:
7201:
7197:
7172:
7168:
7163:
7160:
7155:
7151:
7144:
7140:
7133:
7128:
7124:
7121:
7118:
7102:
7099:
7044:time reversals
7032:state function
7012:thermal energy
6949:
6946:
6915:{\textstyle X}
6911:
6895:{\textstyle X}
6891:
6875:{\textstyle X}
6871:
6855:{\textstyle W}
6851:
6835:{\textstyle V}
6831:
6815:{\textstyle U}
6811:
6795:{\textstyle W}
6791:
6775:{\textstyle V}
6771:
6755:{\textstyle U}
6751:
6714:
6710:
6707:
6701:
6696:
6692:
6689:
6668:
6648:
6644:
6640:
6637:
6632:
6628:
6598:{\textstyle S}
6594:
6562:
6551:trace operator
6537:
6534:
6522:density matrix
6506:
6503:
6478:
6471:
6468:
6462:
6459:
6456:
6450:
6447:
6440:
6434:
6431:
6421:
6416:
6412:
6409:
6406:
6385:
6380:
6376:
6373:
6369:
6362:
6357:
6353:
6350:
6347:
6332:expected value
6305:
6300:
6275:
6271:
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4078:caloric theory
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3445:transformation
3306:Main article:
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3233:heat-potential
3195:climate change
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3072:Multistability
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3005:Self-reference
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2959:Systems theory
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2020:Wolfgang Pauli
2017:
2015:Pascual Jordan
2012:
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1782:Modern physics
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1433:Thermodynamics
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1347:Caloric theory
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327:Free expansion
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264:Control volume
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254:Phase (matter)
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104:The classical
103:
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92:Thermodynamics
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61:
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53:Common symbols
52:
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15:
9:
6:
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18410:Goal-oriented
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18372:Geomorphology
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17932:superfluidity
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17907:
17904:
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17531:
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17524:
17518:
17517:United States
17515:
17513:
17512:South America
17510:
17508:
17505:
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17498:
17495:
17493:
17490:
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17473:
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17465:
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17460:
17458:
17455:
17451:
17448:
17447:
17446:
17445:Energy policy
17443:
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17438:
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17392:
17389:
17387:
17384:
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17375:
17372:
17370:
17369:Solar furnace
17367:
17366:
17365:
17362:
17358:
17355:
17353:
17350:
17349:
17348:
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17340:
17336:
17333:
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17328:
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17326:
17325:Nuclear power
17323:
17319:
17316:
17314:
17311:
17309:
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17279:
17277:
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17262:
17259:
17258:
17256:
17252:
17251:Energy system
17248:
17242:
17239:
17237:
17234:
17232:
17229:
17225:
17222:
17221:
17220:
17217:
17215:
17212:
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17204:Gravitational
17202:
17200:
17197:
17193:
17190:
17188:
17185:
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17133:
17132:Hydrogen fuel
17130:
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17125:
17121:
17118:
17117:
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16978:
16976:
16973:
16971:
16968:
16966:
16963:
16959:
16956:
16955:
16954:
16953:Gravitational
16951:
16949:
16946:
16944:
16941:
16939:
16936:
16934:
16931:
16929:
16926:
16922:
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16851:
16849:
16846:
16844:
16841:
16839:
16836:
16834:
16831:
16829:
16826:
16824:
16823:Heat transfer
16821:
16819:
16818:Heat capacity
16816:
16814:
16811:
16809:
16806:
16804:
16801:
16799:
16796:
16794:
16791:
16790:
16789:
16786:
16784:
16781:
16777:
16774:
16772:
16771:Negative mass
16769:
16768:
16767:
16764:
16762:
16759:
16757:
16754:
16752:
16751:Energy system
16749:
16747:
16744:
16742:
16739:
16735:
16732:
16731:
16730:
16727:
16725:
16722:
16720:
16717:
16716:
16714:
16708:
16702:
16699:
16697:
16694:
16692:
16689:
16688:
16685:
16681:
16674:
16669:
16667:
16662:
16660:
16655:
16654:
16651:
16644:
16641:
16638:
16635:
16631:
16627:
16623:
16622:Sixty Symbols
16619:
16614:
16610:
16607:
16605:
16602:
16600:
16597:
16595:
16592:
16590:
16587:
16586:
16585:
16581:
16578:
16575:
16572:
16569:
16567:
16566:
16561:
16558:
16557:
16546:
16540:
16536:
16535:
16529:
16526:
16522:
16519:
16515:
16511:
16507:
16503:
16497:
16489:
16483:
16479:
16478:
16472:
16468:
16462:
16458:
16453:
16449:
16443:
16439:
16438:
16432:
16428:
16422:
16418:
16417:
16412:
16408:
16404:
16398:
16394:
16390:
16386:
16384:
16381:
16377:
16371:
16367:
16362:
16358:
16352:
16348:
16345:
16341:
16337:
16331:
16327:
16323:
16318:
16314:
16308:
16304:
16299:
16295:
16289:
16284:
16283:
16276:
16272:
16266:
16262:
16258:
16257:Fermi, Enrico
16254:
16250:
16244:
16240:
16235:
16231:
16225:
16217:
16211:
16206:
16205:
16198:
16194:
16188:
16183:
16182:
16175:
16171:
16165:
16157:
16151:
16147:
16142:
16138:
16132:
16128:
16124:
16120:
16116:
16110:
16105:
16104:
16097:
16093:
16087:
16083:
16078:
16074:
16068:
16064:
16060:
16059:Otto Hittmair
16055:
16054:
16035:
16031:
16027:
16022:
16021:
16007:
16003:
15999:
15995:
15991:
15987:
15983:
15979:
15975:
15971:
15965:
15957:
15953:
15949:
15945:
15941:
15937:
15933:
15932:
15924:
15917:
15909:
15905:
15901:
15897:
15893:
15890:. Amsterdam:
15889:
15885:
15884:
15876:
15872:
15866:
15858:
15852:
15845:
15844:
15836:
15828:
15822:
15815:
15814:
15809:
15803:
15794:
15789:
15785:
15781:
15777:
15776:
15771:
15767:
15761:
15746:
15742:
15737:
15732:
15728:
15724:
15720:
15713:
15709:
15703:
15695:
15689:
15685:
15678:
15670:
15664:
15660:
15653:
15645:
15639:
15635:
15628:
15620:
15614:
15610:
15609:
15601:
15593:
15586:
15571:
15565:
15561:
15557:
15550:
15542:
15538:
15534:
15530:
15526:
15522:
15518:
15514:
15509:
15504:
15500:
15496:
15492:
15486:
15478:
15474:
15470:
15466:
15462:
15458:
15454:
15450:
15445:
15440:
15436:
15432:
15425:
15417:
15411:
15403:
15397:
15393:
15392:
15384:
15376:
15372:
15368:
15364:
15360:
15356:
15352:
15348:
15341:
15333:
15329:
15324:
15319:
15315:
15311:
15307:
15303:
15299:
15295:
15291:
15284:
15276:
15272:
15268:
15264:
15260:
15256:
15255:New Scientist
15252:
15245:
15237:
15231:
15227:
15223:
15219:
15218:
15210:
15202:
15198:
15194:
15190:
15186:
15182:
15178:
15174:
15167:
15160:
15152:
15146:
15138:
15132:
15128:
15121:
15113:
15107:
15103:
15096:
15088:
15087:chem.wisc.edu
15084:
15078:
15070:
15064:
15060:
15055:
15054:
15045:
15037:
15033:
15029:
15025:
15021:
15017:
15013:
15009:
15005:
14998:
14989:
14982:
14980:
14979:
14964:
14958:
14954:
14950:
14943:
14935:
14933:9789812832269
14929:
14924:
14923:
14914:
14906:
14902:
14898:
14894:
14890:
14886:
14879:
14871:
14865:
14861:
14854:
14846:
14840:
14836:
14835:
14827:
14825:
14816:
14810:
14806:
14799:
14791:
14785:
14781:
14774:
14766:
14762:
14758:
14754:
14750:
14743:
14735:
14729:
14725:
14724:
14716:
14708:
14704:
14700:
14696:
14692:
14689:(in German).
14688:
14684:
14677:
14669:
14665:
14661:
14657:
14653:
14649:
14644:
14639:
14635:
14631:
14624:
14616:
14610:
14606:
14602:
14595:
14587:
14586:Khaleej Times
14583:
14576:
14568:
14562:
14558:
14557:
14549:
14541:
14537:
14533:
14529:
14525:
14521:
14517:
14513:
14509:
14502:
14494:
14490:
14486:
14482:
14475:
14468:
14460:
14453:
14445:
14441:
14437:
14433:
14429:
14425:
14418:
14416:
14407:
14403:
14399:
14395:
14391:
14387:
14383:
14379:
14372:
14370:
14361:
14355:
14351:
14344:
14342:
14340:
14324:
14320:
14314:
14306:
14300:
14296:
14295:
14287:
14272:
14266:
14262:
14258:
14251:
14235:
14229:
14218:
14211:
14204:
14188:
14184:
14178:
14170:
14164:
14156:
14150:
14146:
14139:
14131:
14127:
14123:
14116:
14114:
14105:
14099:
14095:
14088:
14080:
14074:
14070:
14069:
14061:
14053:
14049:
14045:
14041:
14037:
14033:
14028:
14023:
14019:
14015:
14011:
14007:
14003:
13996:
13994:
13985:
13979:
13974:
13973:
13964:
13956:
13952:
13948:
13944:
13940:
13936:
13932:
13928:
13921:
13913:
13907:
13902:
13901:
13892:
13890:
13881:
13877:
13872:
13867:
13863:
13859:
13855:
13851:
13847:
13843:
13839:
13832:
13824:
13817:
13808:
13803:
13799:
13795:
13791:
13787:
13783:
13776:
13768:
13762:
13754:
13747:
13739:
13735:
13731:
13727:
13723:
13719:
13714:
13709:
13705:
13701:
13694:
13686:
13682:
13678:
13674:
13670:
13666:
13662:
13658:
13653:
13648:
13644:
13640:
13633:
13625:
13619:
13615:
13608:
13600:
13596:
13591:
13586:
13582:
13578:
13573:
13568:
13564:
13560:
13556:
13549:
13541:
13537:
13533:
13529:
13525:
13521:
13517:
13513:
13508:
13503:
13500:(3): 034113.
13499:
13495:
13488:
13480:
13474:
13470:
13463:
13454:
13449:
13445:
13441:
13437:
13433:
13426:
13419:
13403:
13399:
13392:
13384:
13378:
13374:
13373:
13365:
13357:
13351:
13347:
13340:
13332:
13326:
13322:
13318:
13311:
13303:
13297:
13293:
13286:
13278:
13272:
13268:
13263:
13262:
13253:
13251:
13231:
13230:
13222:
13214:
13210:
13206:
13202:
13198:
13194:
13190:
13186:
13182:
13175:
13167:
13161:
13157:
13152:
13151:
13142:
13135:
13131:
13127:
13124:
13119:
13117:
13108:
13102:
13098:
13091:
13083:
13077:
13073:
13068:
13067:
13058:
13056:
13047:
13041:
13037:
13030:
13028:
13026:
13017:
13011:
13007:
13000:
12992:
12986:
12982:
12975:
12967:
12963:
12956:
12948:
12942:
12938:
12937:
12929:
12921:
12917:
12910:
12908:
12899:
12893:
12889:
12882:
12874:
12868:
12864:
12859:
12858:
12849:
12841:
12835:
12831:
12826:
12825:
12816:
12808:
12802:
12798:
12791:
12776:
12772:
12770:
12762:
12747:
12743:
12736:
12720:
12719:
12712:
12704:
12697:
12695:
12687:
12672:
12652:
12642:
12640:0-691-02350-6
12636:
12632:
12627:
12626:
12620:
12614:
12612:
12604:
12601:
12597:
12593:
12589:
12584:
12580:
12576:
12572:
12568:
12562:
12558:
12554:
12550:
12546:
12543:(in German).
12542:
12538:
12531:
12529:
12521:
12517:
12511:
12504:
12497:
12492:
12488:
12484:
12480:
12476:
12472:
12469:(in German).
12468:
12461:
12459:
12450:
12444:
12436:
12429:
12413:
12407:
12400:
12399:0-444-87009-1
12396:
12392:
12388:
12383:
12375:
12371:
12365:
12360:
12359:
12353:
12352:Truesdell, C.
12347:
12339:
12335:
12331:
12327:
12323:
12319:
12315:
12308:
12304:
12289:
12285:
12274:
12271:
12269:
12266:
12264:
12261:
12259:
12256:
12253:
12250:
12248:
12245:
12243:
12240:
12238:
12235:
12233:
12230:
12228:
12225:
12223:
12220:
12218:
12215:
12213:
12210:
12208:
12205:
12203:
12200:
12198:
12195:
12193:
12190:
12189:
12182:
12180:
12177:
12173:
12168:
12166:
12162:
12158:
12154:
12153:
12147:
12143:
12139:
12135:
12131:
12126:
12122:
12112:
12110:
12105:
12103:
12099:
12094:
12092:
12087:
12083:
12079:
12078:event horizon
12075:
12071:
12067:
12063:
12062:Roger Penrose
12058:
12056:
12045:
12041:
12039:
12029:
12027:
12023:
12022:arrow of time
12013:
12011:
12007:
12003:
11999:
11995:
11985:
11981:
11967:
11947:
11922:
11895:
11891:
11880:
11877:
11860:
11846:
11843:
11840:
11834:
11828:
11820:
11811:
11805:
11802:
11782:
11771:
11746:
11726:
11712:
11698:
11678:
11670:
11667:which is the
11653:
11649:
11646:
11643:
11640:
11637:
11617:
11596:
11592:
11589:
11586:
11579:
11575:
11570:
11567:
11562:
11558:
11551:
11546:
11543:
11540:
11536:
11532:
11529:
11526:
11518:
11502:
11498:
11494:
11491:
11488:
11480:
11479:
11462:
11453:
11449:
11447:
11443:
11420:
11416:
11409:
11405:
11402:
11394:
11390:
11383:
11377:
11372:
11369:
11366:
11362:
11358:
11355:
11349:
11343:
11321:
11317:
11308:
11304:
11300:
11296:
11290:
11287:
11283:
11279:
11272:
11265:
11261:
11257:
11247:
11245:
11241:
11237:
11232:
11226:
11208:
11204:
11199:
11196:
11191:
11187:
11180:
11176:
11164:
11160:
11157:
11154:
11132:
11128:
11119:
11115:
11110:
11108:
11084:
11075:
11046:
11024:
10999:
10989:
10983:
10980:
10977:
10968:
10961:
10937:
10933:
10930:
10927:
10919:
10915:
10911:
10905:
10895:
10879:
10875:
10851:
10848:
10845:
10820:
10816:
10808:in the state
10795:
10775:
10755:
10735:
10713:
10709:
10686:
10682:
10673:
10669:
10665:
10661:
10651:
10649:
10644:
10641:
10637:
10636:effectiveness
10630:
10624:
10622:
10618:
10614:
10609:
10606:shows, in an
10605:
10601:
10597:
10592:
10590:
10586:
10582:
10558:
10548:
10526:
10517:
10493:
10464:
10433:
10421:
10415:
10412:
10409:
10360:
10348:
10342:
10305:
10301:
10297:
10293:
10289:
10285:
10279:
10269:
10263:
10259:
10255:
10252:
10249:
10246:a measure of
10245:
10244:
10243:
10235:
10227:
10204:
10185:
10175:
10158:
10146:
10122:
10113:
10097:
10084:
10065:
10055:
10038:
10026:
10002:
9993:
9988:
9978:
9961:
9957:
9953:
9948:
9945:
9942:
9939:
9936:
9929:
9925:
9921:
9916:
9913:
9902:
9898:
9895:
9892:
9865:
9861:
9857:
9852:
9849:
9846:
9843:
9840:
9833:
9829:
9825:
9820:
9817:
9806:
9802:
9799:
9796:
9785:
9780:
9778:
9773:
9751:
9726:
9722:
9718:
9713:
9710:
9699:
9695:
9692:
9689:
9677:
9675:
9651:
9642:
9641:heat capacity
9619:
9615:
9611:
9606:
9603:
9592:
9588:
9585:
9582:
9572:
9571:
9570:
9556:
9534:
9530:
9515:
9513:
9509:
9493:
9485:
9469:
9445:
9441:
9437:
9432:
9429:
9426:
9423:
9420:
9417:
9410:
9406:
9402:
9397:
9394:
9391:
9388:
9385:
9382:
9359:
9352:and pressure
9339:
9317:
9313:
9305:and pressure
9290:
9286:
9277:
9267:
9259:
9245:
9242:
9222:
9219:
9177:
9174:
9161:
9147:
9125:
9121:
9100:
9078:
9071:
9068:
9041:
9037:
9032:
9026:
9019:
9016:
9006:
9002:
8981:
8977:
8970:
8967:
8955:
8953:
8949:
8945:
8941:
8937:
8904:
8901:
8877:
8873:
8866:
8863:
8838:
8828:
8802:
8795:
8792:
8765:
8755:
8746:
8739:
8736:
8726:
8721:
8718:
8715:
8711:
8672:
8669:
8662:
8657:
8652:
8649:
8642:
8637:
8627:
8618:
8611:
8608:
8598:
8593:
8590:
8587:
8583:
8579:
8573:
8563:
8535:
8515:
8494:
8474:
8454:
8434:
8414:
8405:
8401:
8388:
8372:
8365:
8360:
8357:
8341:
8321:
8317:
8310:
8307:
8281:
8278:
8272:
8241:
8238:
8211:
8208:
8197:
8193:
8189:
8185:
8177:
8172:
8163:
8161:
8157:
8153:
8149:
8145:
8141:
8136:
8135:
8128:
8118:
8104:
8093:
8077:
8054:
8045:
8042:
8039:
8033:
8030:
8007:
7987:
7976:
7937:
7930:
7886:
7879:
7847:
7823:
7811:
7793:
7789:
7771:
7753:
7751:
7750:molar entropy
7747:
7742:
7738:
7733:
7730:
7726:
7722:
7718:
7708:
7706:
7702:
7697:
7683:
7663:
7652:
7649:
7646:
7635:
7632:
7629:
7604:
7584:
7576:
7560:
7549:
7534:
7532:
7528:
7523:
7519:
7517:
7516:
7497:
7493:
7472:
7467:
7463:
7442:
7438:
7434:
7431:
7411:
7408:
7388:
7380:
7376:
7371:
7369:
7364:
7362:
7358:
7354:
7350:
7345:
7331:
7328:
7325:
7324:
7322:
7319:
7317:
7313:
7296:
7291:
7287:
7283:
7279:
7276:
7268:
7264:
7260:
7256:
7252:
7248:
7230:
7212:
7208:
7202:
7199:
7170:
7166:
7161:
7158:
7153:
7149:
7142:
7138:
7126:
7122:
7119:
7116:
7108:
7098:
7096:
7091:
7087:
7085:
7080:
7076:
7072:
7071:heat capacity
7068:
7063:
7061:
7060:arrow of time
7057:
7053:
7049:
7045:
7041:
7037:
7033:
7028:
7026:
7021:
7016:
7013:
7009:
7004:
7002:
6998:
6994:
6990:
6986:
6981:
6979:
6970:
6965:
6959:
6954:
6945:
6943:
6938:
6936:
6932:
6928:
6923:
6909:
6889:
6869:
6849:
6829:
6809:
6789:
6769:
6749:
6739:
6736:
6731:
6729:
6708:
6705:
6694:
6690:
6687:
6642:
6638:
6635:
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6613:
6612:
6606:
6592:
6584:
6580:
6576:
6560:
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6476:
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6438:
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6410:
6407:
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6264:
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6256:
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6229:
6225:
6222:
6219:
6211:
6193:
6189:
6180:
6175:
6173:
6169:
6165:
6161:
6158:(Jâ
K) in the
6157:
6153:
6149:
6144:
6142:
6138:
6134:
6130:
6126:
6122:
6118:
6113:
6111:
6106:
6100:
6090:
6088:
6084:
6080:
6063:
6057:
6054:
6047:and at least
6034:
6011:
5991:
5980:
5976:
5972:
5967:
5953:
5950:
5947:
5939:
5938:absolute zero
5935:
5930:
5926:
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5902:
5884:
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5842:
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5595:
5594:
5590:
5580:
5578:
5574:
5570:
5566:
5561:
5559:
5555:
5554:Brayton cycle
5551:
5547:
5543:
5527:
5524:
5507:
5500:
5483:
5457:
5454:
5443:
5419:
5416:
5403:
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5372:
5360:
5337:
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5290:
5278:
5272:
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5119:
5114:
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5025:
5012:
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4316:
4311:
4297:
4285:
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4253:
4240:
4227:
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4212:
4205:
4202:
4174:
4153:
4145:
4141:
4117:
4088:
4079:
4055:
4026:
4005:
3998:
3994:
3990:
3966:
3937:
3928:
3904:
3875:
3866:
3862:
3858:
3848:
3844:
3842:
3838:
3820:
3802:
3798:
3792:
3789:
3776:
3775:heat transfer
3772:
3759:
3751:
3747:
3720:
3716:
3708:
3704:
3691:
3671:
3669:
3668:line integral
3665:
3661:
3657:
3656:ideal gas law
3652:
3648:
3644:
3640:
3636:
3626:
3624:
3620:
3616:
3610:
3608:
3604:
3603:Willard Gibbs
3598:
3587:
3585:
3580:
3578:
3574:
3570:
3564:
3561:
3557:
3545:
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3414:
3410:
3406:
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3397:
3392:
3387:
3382:
3380:
3376:
3372:
3368:
3364:
3359:
3357:
3353:
3352:Count Rumford
3349:
3345:
3341:
3337:
3333:
3332:
3327:
3323:
3319:
3318:Lazare Carnot
3315:
3309:
3301:
3297:
3288:
3286:
3282:
3278:
3274:
3270:
3266:
3261:
3256:
3254:
3250:
3246:
3242:
3238:
3234:
3230:
3226:
3221:
3219:
3215:
3211:
3206:
3204:
3200:
3196:
3192:
3188:
3184:
3180:
3176:
3172:
3168:
3164:
3160:
3156:
3152:
3141:
3136:
3134:
3129:
3127:
3122:
3121:
3119:
3118:
3112:
3109:
3107:
3103:
3098:
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3065:
3061:
3057:
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3028:
3026:
3022:
3018:
3014:
3010:
3006:
3002:
2998:
2994:
2990:
2986:
2985:Goal-oriented
2982:
2978:
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2948:Geomorphology
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2614:
2612:
2609:
2607:
2604:
2602:
2599:
2597:
2594:
2592:
2589:
2587:
2586:J. J. Thomson
2584:
2582:
2579:
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2457:
2454:
2452:
2449:
2447:
2444:
2442:
2439:
2437:
2434:
2432:
2431:van der Waals
2429:
2427:
2424:
2422:
2419:
2417:
2414:
2412:
2409:
2407:
2404:
2402:
2399:
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2239:
2236:
2234:
2231:
2229:
2226:
2224:
2221:
2219:
2216:
2214:
2211:
2209:
2206:
2204:
2201:
2199:
2196:
2194:
2191:
2189:
2186:
2184:
2181:
2179:
2176:
2172:
2169:
2167:
2164:
2162:
2159:
2158:
2157:
2154:
2152:
2149:
2147:
2144:
2142:
2139:
2137:
2134:
2132:
2129:
2128:
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2121:
2114:
2111:
2109:
2106:
2104:
2101:
2099:
2096:
2094:
2091:
2089:
2086:
2084:
2081:
2079:
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2071:
2069:
2066:
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2061:
2059:
2056:
2055:
2049:
2048:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1982:
1976:
1975:
1971:
1967:
1949:
1946:
1942:
1937:
1933:
1928:
1925:
1921:
1914:
1909:
1906:
1902:
1875:
1867:
1863:
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1680:
1675:
1667:
1666:
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1657:
1654:
1652:
1649:
1647:
1646:Self-assembly
1644:
1642:
1639:
1638:
1632:
1631:
1623:
1620:
1618:
1617:van der Waals
1615:
1613:
1610:
1608:
1605:
1603:
1600:
1598:
1595:
1593:
1590:
1588:
1585:
1583:
1580:
1578:
1575:
1573:
1570:
1568:
1565:
1563:
1560:
1558:
1555:
1553:
1550:
1548:
1545:
1543:
1542:von Helmholtz
1540:
1538:
1535:
1533:
1530:
1528:
1525:
1523:
1520:
1518:
1515:
1513:
1510:
1508:
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1498:
1495:
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1449:
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1445:
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1436:
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1430:
1428:
1427:
1423:
1422:
1416:
1415:
1408:
1405:
1404:
1397:
1394:
1393:
1386:
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1383:
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1376:
1371:
1368:
1366:
1363:
1361:
1357:
1353:
1352:
1348:
1345:
1344:
1342:
1341:
1337:
1336:
1330:
1327:
1325:
1322:
1320:
1317:
1315:
1312:
1310:
1307:
1305:
1302:
1300:
1297:
1296:
1294:
1293:
1290:
1287:
1286:
1281:
1278:
1277:
1273:
1270:
1268:
1265:
1263:
1260:
1259:
1257:
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1251:
1242:
1239:
1238:
1234:
1233:
1213:
1210:
1207:
1204:
1201:
1195:
1192:
1189:
1183:
1175:
1172:
1158:
1155:
1152:
1149:
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1140:
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1134:
1128:
1120:
1117:
1103:
1100:
1097:
1094:
1091:
1085:
1082:
1079:
1073:
1065:
1062:
1045:
1042:
1039:
1033:
1025:
1022:
1021:
1016:
1013:
1011:
1008:
1007:
1003:
998:
997:
990:
989:
985:
983:
980:
978:
975:
973:
970:
969:
965:
964:Ideal gas law
962:
960:
957:
955:
952:
950:
947:
946:
942:
937:
936:
910:
900:
886:
879:
878:
863:
853:
839:
832:
831:
828:
814:
811:
804:
801:
798:
797:
778:
768:
754:
747:
746:
731:
721:
707:
700:
699:
696:
682:
679:
676:
669:
666:
663:
662:
643:
633:
619:
612:
611:
596:
586:
572:
565:
564:
561:
547:
544:
537:
534:
531:
530:
524:
521:
520:
517:
512:
511:
500:
497:
495:
494:Vapor quality
492:
490:
489:
484:
481:
479:
478:
473:
470:
467:
463:
462:
457:
454:
453:
452:
451:
448:
445:
444:
438:
435:
433:
430:
429:
427:
426:
423:
420:
419:
414:
411:
409:
406:
405:
404:
403:
399:
395:
388:
383:
382:
371:
368:
366:
363:
361:
358:
357:
356:
355:
352:
349:
348:
343:
340:
338:
335:
333:
332:Reversibility
330:
328:
325:
323:
320:
318:
315:
313:
310:
308:
305:
303:
300:
298:
295:
293:
290:
288:
285:
284:
283:
282:
279:
276:
275:
270:
267:
265:
262:
260:
257:
255:
252:
250:
247:
245:
242:
240:
237:
235:
232:
231:
230:
229:
226:
223:
222:
217:
214:
212:
209:
207:
206:Closed system
204:
203:
200:
195:
194:
186:
183:
181:
178:
176:
173:
171:
168:
167:
163:
158:
157:
150:
146:
143:
142:
138:
135:
133:
130:
128:
125:
123:
120:
119:
112:
111:
107:
101:
97:
96:
93:
90:
89:
81:
79:
72:
68:
66:
62:
59:
56:
50:
45:
42:
37:
30:
23:
18424:
18236:Graph theory
18165:Evolvability
17915:Applications
17877:
17866:size scaling
17596:
17584:
17572:
17560:
17342:Oil refinery
17286:Cogeneration
17219:Nuclear fuel
17025:Quintessence
16813:Free entropy
16802:
16746:Energy level
16710:Fundamental
16621:
16565:Scholarpedia
16563:
16533:
16509:
16476:
16456:
16436:
16415:
16392:
16365:
16347:
16344:
16321:
16302:
16281:
16260:
16238:
16203:
16180:
16145:
16126:
16102:
16081:
16063:WĂ€rmetheorie
16062:
16038:. Retrieved
16034:the original
16029:
16009:. Retrieved
15984:(3): 100â7.
15981:
15977:
15964:
15935:
15929:
15916:
15887:
15881:
15865:
15842:
15835:
15812:
15802:
15779:
15773:
15760:
15748:. Retrieved
15726:
15702:
15683:
15677:
15658:
15652:
15633:
15627:
15607:
15600:
15591:
15585:
15573:. Retrieved
15559:
15549:
15498:
15495:Phys. Rev. E
15494:
15491:Callaway DJE
15485:
15434:
15430:
15424:
15390:
15383:
15350:
15346:
15340:
15297:
15293:
15283:
15261:(3334): 15.
15258:
15254:
15244:
15220:. Springer.
15216:
15209:
15176:
15172:
15159:
15126:
15120:
15101:
15095:
15086:
15077:
15052:
15044:
15011:
15007:
14997:
14988:
14976:
14973:
14966:. Retrieved
14952:
14942:
14921:
14913:
14888:
14884:
14878:
14859:
14853:
14833:
14804:
14798:
14779:
14773:
14756:
14752:
14742:
14722:
14715:
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14686:
14676:
14633:
14629:
14623:
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14548:
14515:
14511:
14501:
14484:
14480:
14467:
14452:
14427:
14423:
14381:
14377:
14349:
14326:. Retrieved
14322:
14313:
14293:
14286:
14274:. Retrieved
14260:
14250:
14238:. Retrieved
14228:
14217:the original
14203:
14191:. Retrieved
14187:the original
14177:
14144:
14138:
14121:
14093:
14087:
14067:
14060:
14009:
14005:
13971:
13963:
13930:
13926:
13920:
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13845:
13841:
13831:
13822:
13816:
13789:
13785:
13775:
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13746:
13703:
13699:
13693:
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13638:
13632:
13613:
13607:
13562:
13558:
13548:
13497:
13493:
13487:
13468:
13462:
13435:
13431:
13418:
13406:. Retrieved
13402:the original
13391:
13371:
13364:
13345:
13339:
13316:
13310:
13291:
13285:
13260:
13237:. Retrieved
13228:
13221:
13188:
13184:
13174:
13149:
13141:
13133:
13096:
13090:
13065:
13035:
13005:
12999:
12980:
12974:
12965:
12961:
12955:
12935:
12928:
12919:
12915:
12887:
12881:
12856:
12848:
12823:
12815:
12796:
12790:
12778:. Retrieved
12774:
12768:
12761:
12749:. Retrieved
12745:
12735:
12723:. Retrieved
12717:
12711:
12702:
12644:
12624:
12599:
12595:
12591:
12587:
12582:
12578:
12574:
12570:
12566:
12564:
12544:
12540:
12510:
12502:
12470:
12466:
12434:
12428:
12416:. Retrieved
12406:
12390:
12382:
12372:– via
12357:
12346:
12321:
12317:
12307:
12288:
12247:Info-metrics
12237:Free entropy
12232:Entropy unit
12169:
12151:
12128:
12106:
12095:
12059:
12051:
12042:
12037:
12035:
12019:
11991:
11982:
11718:
11476:
11454:
11450:
11302:
11292:
11274:
11269:
11227:
11111:
10907:
10657:
10645:
10639:
10635:
10633:
10628:
10620:
10617:Peter Atkins
10599:
10595:
10593:
10578:
10281:
10267:
10241:
10233:
10112:vaporization
9984:
9781:
9774:
9678:
9638:
9521:
9273:
9265:
9162:
8956:
8361:
8188:open systems
8181:
8176:steady-state
8132:
8130:
7812:
7754:
7749:
7734:
7714:
7698:
7574:
7551:
7537:Applications
7524:
7520:
7513:
7372:
7365:
7341:
7320:
7104:
7092:
7088:
7064:
7029:
7017:
7005:
6997:combinations
6982:
6978:Carnot cycle
6975:
6941:
6939:
6924:
6740:
6732:
6609:
6607:
6325:
6176:
6145:
6120:
6114:
6102:
5968:
5931:
5927:
5856:
5712:
5706:
5696:
5684:Carnot cycle
5665:
5642:
5562:
5542:Carnot cycle
5230:
4954:
4949:
4722:
4344:
3861:Carnot cycle
3854:
3851:Carnot cycle
3845:
3841:Carnot cycle
3752:
3709:
3679:
3677:
3664:Carnot cycle
3632:
3612:
3606:
3600:
3595:
3582:
3576:
3572:
3568:
3566:
3562:
3543:
3539:
3535:
3511:
3509:
3495:
3491:
3453:
3448:
3444:
3434:
3430:
3420:
3417:Isaac Newton
3405:working body
3390:
3383:
3371:conservation
3360:
3356:engine cycle
3340:motive power
3329:
3328:, published
3321:
3313:
3311:
3275:law, with a
3257:
3252:
3248:
3244:
3243:, in German
3240:
3232:
3228:
3222:
3218:irreversible
3207:
3150:
3149:
3100:
3050:
2976:
2971:
2917:
2898:Evolvability
2863:
2819:Graph theory
2801:
2738:
2263:Astrophysics
2243:Neurophysics
2146:Mathematical
2136:Experimental
2097:
1725:Introduction
1715:
1507:Carathéodory
1438:Heat engines
1410:
1399:
1388:
1370:Motive power
1355:
1015:Free entropy
986:
486:
485: /
475:
474: /
466:introduction
460:
459:
458: /
397:
360:Heat engines
147: /
65:SI unit
57:
41:
18435:Autopoiesis
18430:Cybernetics
18420:Sensemaking
18390:Homeostasis
18352:Percolation
18314:Bifurcation
18289:Phase space
18175:Game theory
18032:Collective
17906:von Neumann
17776:force field
17768:percolation
17598:WikiProject
17418:Agriculture
17347:Solar power
17313:Tidal power
17187:Natural gas
17177:Fossil fuel
17120:Latent heat
17088:Electricity
16626:Brady Haran
16618:"S Entropy"
16030:stejfree.sk
16011:23 November
15942:: 544â551.
15894:: 115â128.
15786:: 203â223.
15353:: 444â457.
14636:(1): 1â96.
14276:5 September
14210:"Third Law"
13645:(1): 1â10.
12775:web.mit.edu
12725:26 February
12418:24 February
12387:Brush, S.G.
12258:Phase space
12179:Herman Daly
12070:black holes
12038:et al.
11715:Measurement
11286:attenuation
9985:Reversible
8094:change and
7379:useful work
7001:microstates
6993:probability
6991:has higher
6583:Hamiltonian
6579:eigenstates
6179:logarithmic
6133:microstates
6129:microstates
6121:mixedupness
5638:Temperature
4146:, the work
3837:quasistatic
3750:temperature
3584:Leon Cooper
3440:Verwandlung
3379:dissipation
3367:James Joule
3344:water wheel
3326:Sadi Carnot
3273:logarithmic
3092:Game theory
3076:Bifurcation
3056:Phase space
3021:Sensemaking
2989:Homeostasis
2968:Autopoiesis
2963:cybernetics
2931:Percolation
2526:von Neumann
2391:Schrödinger
2223:Statistical
2141:Theoretical
2093:Information
1966:Schrödinger
1329:Synergetics
1010:Free energy
456:Temperature
317:Quasistatic
312:Isenthalpic
269:Instruments
259:Equilibrium
211:Open system
145:Equilibrium
127:Statistical
18460:Categories
18246:Robustness
18226:Centrality
18112:adaptation
18010:Background
17763:Heisenberg
17381:Wind power
17303:Hydropower
17254:components
17209:Hydropower
17199:Geothermal
17149:Sound wave
17060:Zero-point
16990:Mechanical
16975:Ionization
16948:Electrical
16843:Negentropy
16724:Energetics
14518:(2): 187.
13792:(4): 405.
13572:2006.00485
13565:: 105230.
13507:1903.02121
13408:27 January
12520:0198642148
12369:0387904034
12300:References
12252:Negentropy
12138:progenitor
12132:economist
12119:See also:
12055:heat death
12036:Chiavazzo
10768:such that
10640:usefulness
10629:usefulness
9160:-th port.
8152:zettabytes
8125:See also:
7808:298 K
7761:298 K
7261:, and the
6937:property.
6148:dimensions
6137:macrostate
6081:(though a
5180:is either
3989:isothermal
3927:isothermal
3863:that is a
3155:scientific
3060:Attractors
2855:adaptation
2827:Robustness
2811:Centrality
2643:Categories
2436:Heisenberg
2396:de Broglie
2346:Rutherford
2341:Sommerfeld
2295:Scientists
2238:Biophysics
2088:Randomness
2025:Paul Dirac
1995:Niels Bohr
1985:Max Planck
1641:Nucleation
1485:Scientists
1289:Philosophy
1002:Potentials
365:Heat pumps
322:Polytropic
307:Isentropic
297:Isothermal
18486:Asymmetry
18294:Attractor
18107:Evolution
18017:Emergence
17886:Boltzmann
17809:H-theorem
17687:Ensembles
17492:Australia
17428:Transport
17423:Computing
17391:Wind farm
17318:Wave farm
17192:Petroleum
17172:Bioenergy
17144:Radiation
17083:Capacitor
17005:Potential
16560:"Entropy"
16496:cite book
16305:. Dover.
16224:cite book
16181:Chemistry
16164:cite book
15908:154728333
15575:31 August
15410:cite book
15375:0378-4371
15145:cite book
15036:212779004
15028:1754-5692
14968:31 August
14905:118726162
14707:118230148
14668:119620408
14493:1369-5614
14406:122424225
14240:17 August
14193:17 August
14163:cite book
14052:206531385
14036:0036-8075
13786:Phys. Rev
13761:cite book
13738:119224112
13713:1311.2068
13706:: 17â21.
13652:0903.4147
13599:221978379
13540:118981017
13239:17 August
13213:0002-9505
12769:Lost Work
12746:chem1.com
12686:helpful."
12443:cite book
12115:Economics
12048:Cosmology
12010:evolution
11867:⇒
11861:⋯
11855:⇒
11826:∂
11818:∂
11775:→
11650:
11593:
11571:
11537:∑
11533:−
11406:
11363:∑
11359:−
11200:
11177:∑
11161:−
11028:^
11025:ρ
10993:^
10990:ρ
10984:
10978:×
10972:^
10969:ρ
10934:−
10852:λ
10849:−
10796:λ
10756:λ
10575:disperse.
10456:In which
10416:−
10182:Δ
10155:Δ
10062:Δ
10035:Δ
9949:
9937:−
9917:
9890:Δ
9853:
9821:
9794:Δ
9714:
9687:Δ
9607:
9580:Δ
9433:
9421:−
9398:
9380:Δ
9276:ideal gas
9243:≥
9223:˙
9178:˙
9072:˙
9020:˙
9003:∑
8971:˙
8952:viscosity
8905:˙
8867:˙
8832:^
8796:˙
8759:^
8740:˙
8712:∑
8673:˙
8653:˙
8631:^
8612:˙
8584:∑
8495:θ
8475:θ
8455:θ
8435:θ
8402:θ
8373:θ
8311:˙
8282:˙
8242:˙
8212:˙
8162:in 2007.
8156:petabytes
8102:Δ
8075:Δ
8052:Δ
8043:−
8037:Δ
8028:Δ
7985:Δ
7934:Δ
7883:Δ
7844:Δ
7821:Δ
7737:extensive
7650:−
7432:δ
7409:δ
7209:δ
7162:
7139:∑
7123:−
7040:chemistry
6713:Ω
6709:
6667:Ω
6647:Ω
6505:^
6502:ρ
6470:^
6467:ρ
6461:
6455:×
6449:^
6446:ρ
6411:−
6375:
6352:−
6265:
6242:∑
6226:−
6061:Δ
6058:⋅
6032:Δ
5989:Δ
5881:δ
5855:, called
5792:δ
5782:∫
5731:δ
5725:∮
5680:extensive
5504:Δ
5480:Δ
5440:Δ
5273:−
5123:−
5097:Δ
5053:Δ
5029:Δ
4995:−
4964:−
4925:δ
4767:−
4692:−
4686:δ
4613:−
4598:−
4546:−
4535:Σ
4527:−
4412:−
4384:Σ
4280:−
4254:⋅
4224:−
3799:δ
3717:δ
3506:Etymology
3468:ideal gas
3187:sociology
3183:economics
3179:cosmology
3171:chemistry
2851:Evolution
2718:Emergence
2631:Uhlenbeck
2621:Zeilinger
2581:Gell-Mann
2311:Becquerel
2268:Cosmology
1950:ν
1947:μ
1938:κ
1929:ν
1926:μ
1918:Λ
1910:ν
1907:μ
1882:⟩
1864:ψ
1840:ℏ
1831:⟩
1813:ψ
1801:^
1622:Waterston
1572:von Mayer
1527:de Donder
1517:Clapeyron
1497:Boltzmann
1492:Bernoulli
1453:Education
1424:Timelines
1208:−
1153:−
941:Equations
908:∂
861:∂
812:α
776:∂
729:∂
683:−
677:β
641:∂
594:∂
302:Adiabatic
292:Isochoric
278:Processes
239:Ideal gas
122:Classical
18400:Feedback
18208:Networks
18034:behavior
17896:Tsallis
17562:Category
17127:Hydrogen
17093:Enthalpy
16995:Negative
16985:Magnetic
16970:Internal
16928:Chemical
16793:Enthalpy
16712:concepts
16628:for the
16413:(2005).
16391:(2013).
16259:(1937).
16123:Ben-Naim
16061:(1992).
16040:13 April
16006:13441670
15998:16121860
15972:(2015).
15940:Elsevier
15892:Elsevier
15873:(2007).
15784:Elsevier
15710:(2004).
15469:10055336
15332:25556697
15300:: 7611.
15201:12418973
14765:24923125
14603:(1989).
14540:97102995
14487:(1): 4.
14044:21310967
13955:18081336
13880:25662746
13848:: 8323.
13685:22204063
13677:19658663
13532:31325924
13126:Archived
12621:(1960).
12603:scheint.
12596:Entropie
12592:Entropie
12389:(1976).
12354:(1980).
12185:See also
12159:form an
11671:, where
11478:a priori
11336:so that:
10596:disorder
10290:, or of
10288:disorder
9057:, where
8950:such as
8334:, where
8160:exabytes
8148:exabytes
8144:exabytes
8140:exabytes
8092:enthalpy
7757:0 K
7703:and the
7297:⟩
7284:⟨
7084:enthalpy
6933:and the
6659:, where
6384:⟩
6368:⟨
6328:integral
5610:Pressure
5160:, where
4140:Clausius
3519:Entropie
3375:friction
2981:Feedback
2914:Fractals
2793:Networks
2626:Goudsmit
2616:Lawrence
2611:Chadwick
2606:Shockley
2566:'t Hooft
2516:Millikan
2501:Poincaré
2491:LemaĂźtre
2361:Einstein
2203:Particle
2125:Branches
2108:Particle
2058:Topology
2052:Concepts
2000:Max Born
1979:Founders
1674:Category
1612:Thompson
1522:Clausius
1502:Bridgman
1356:Vis viva
1338:Theories
1272:Gas laws
1064:Enthalpy
472:Pressure
287:Isobaric
244:Real gas
132:Chemical
115:Branches
82:kgâ
mâ
sâ
K
36:Enthalpy
18466:Entropy
18425:Entropy
18241:Scaling
17891:Shannon
17878:Entropy
17574:Commons
17402:Use and
17261:Biomass
17231:Radiant
17078:Battery
17050:Thermal
17045:Surface
17030:Radiant
17000:Phantom
16980:Kinetic
16958:Binding
16938:Elastic
16921:Nuclear
16916:Binding
16803:Entropy
16701:Outline
16691:History
16204:Physics
15944:Bibcode
15750:28 June
15741:Bibcode
15541:7115890
15533:9964684
15513:Bibcode
15477:9329564
15449:Bibcode
15355:Bibcode
15323:5154591
15302:Bibcode
15263:Bibcode
15181:Bibcode
14648:Bibcode
14520:Bibcode
14432:Bibcode
14386:Bibcode
14126:Bibcode
14014:Bibcode
14006:Science
13935:Bibcode
13871:4321171
13850:Bibcode
13794:Bibcode
13718:Bibcode
13657:Bibcode
13577:Bibcode
13512:Bibcode
13440:Bibcode
13432:Entropy
13193:Bibcode
12966:eq.(64)
12600:Energie
12549:Bibcode
12475:Bibcode
12326:Bibcode
12102:quantum
12066:gravity
12032:Biology
11299:Entropy
11105:is the
11072:is the
11043:is the
10294:, in a
9992:melting
9506:is the
8174:During
8134:Science
8090:is the
7977:change
7036:physics
6319:is the
5857:entropy
5643:Entropy
5571:, e.g.
4956:stages:
4950:entropy
3987:during
3925:during
3623:phonons
3577:entropy
3573:entropy
3540:entropy
3513:entropy
3449:entropy
3431:turning
3336:caloric
3291:History
3249:entropy
3175:physics
3151:Entropy
3025:Variety
2977:Entropy
2823:Scaling
2601:Bardeen
2571:Veltman
2541:Feynman
2511:Penrose
2506:Wheeler
2496:Thomson
2481:Hawking
2456:Hilbert
2451:Moseley
2411:Compton
2386:Kramers
2366:Wilczek
2316:Lorentz
2306:Röntgen
2208:Nuclear
2131:Applied
2098:Entropy
1730:History
1597:Smeaton
1592:Rankine
1582:Onsager
1567:Maxwell
1562:Massieu
1267:Entropy
1262:General
1253:History
1243:Culture
1240:History
464: (
461:Entropy
398:italics
199:Systems
47:Entropy
18231:Motifs
17740:Models
17648:Theory
17586:Portal
17507:Mexico
17502:Europe
17497:Canada
17482:Africa
17405:supply
17214:Marine
17103:Fossil
17055:Vacuum
16808:Exergy
16729:Energy
16680:Energy
16541:
16516:
16484:
16463:
16444:
16423:
16399:
16372:
16353:
16332:
16309:
16290:
16267:
16245:
16212:
16189:
16152:
16133:
16111:
16088:
16069:
16004:
15996:
15906:
15853:
15823:
15690:
15665:
15640:
15615:
15566:
15539:
15531:
15475:
15467:
15398:
15373:
15330:
15320:
15232:
15199:
15133:
15108:
15065:
15034:
15026:
14981:].
14959:
14930:
14903:
14866:
14841:
14811:
14786:
14763:
14730:
14705:
14666:
14611:
14563:
14538:
14491:
14404:
14356:
14328:22 May
14301:
14267:
14151:
14100:
14075:
14050:
14042:
14034:
13980:
13953:
13908:
13878:
13868:
13736:
13683:
13675:
13620:
13597:
13538:
13530:
13475:
13379:
13352:
13327:
13298:
13273:
13211:
13162:
13103:
13078:
13042:
13012:
12987:
12943:
12894:
12869:
12836:
12803:
12780:21 May
12751:21 May
12637:
12518:
12397:
12366:
12123:, and
12008:, and
11870:
11864:
11858:
11852:
11262:, and
11014:where
10949:
10518:, and
10143:, the
10023:, the
9486:) and
8703:where
8194:, and
8067:where
8049:
7656:
7639:
7515:Exergy
7257:, the
7253:, the
6491:where
6426:
6290:where
6156:kelvin
6152:joules
5923:kelvin
5703:system
5630:Strain
5623:Stress
5615:Volume
5550:Diesel
4144:Kelvin
3544:energy
3462:, and
3435:change
3287:(SI).
3279:, the
3197:, and
2815:Motifs
2705:Topics
2556:Lenard
2476:Wigner
2466:Jordan
2446:Zeeman
2421:Walton
2321:Planck
2301:Witten
2198:Atomic
2078:Matter
2073:Energy
1587:Planck
1577:Nernst
1552:Kelvin
1512:Carnot
802:
667:
535:
477:Volume
392:Note:
351:Cycles
180:Second
170:Zeroth
18304:Chaos
17949:chaos
17901:RĂ©nyi
17758:Potts
17753:Ising
17526:Misc.
17236:Solar
17040:Sound
16909:Types
16783:Power
16734:Units
16696:Index
16002:S2CID
15926:(PDF)
15904:S2CID
15878:(PDF)
15731:arXiv
15717:. In
15715:(PDF)
15537:S2CID
15503:arXiv
15473:S2CID
15439:arXiv
15197:S2CID
15169:(PDF)
15032:S2CID
14901:S2CID
14761:JSTOR
14703:S2CID
14664:S2CID
14638:arXiv
14536:S2CID
14477:(PDF)
14402:S2CID
14220:(PDF)
14213:(PDF)
14048:S2CID
13951:S2CID
13734:S2CID
13708:arXiv
13681:S2CID
13647:arXiv
13595:S2CID
13567:arXiv
13536:S2CID
13502:arXiv
13428:(PDF)
13233:(PDF)
13132:. In
12865:â85.
12280:Notes
11519:) is:
10600:chaos
10292:chaos
10284:order
9484:moles
9462:Here
9208:that:
8385:in a
6983:In a
6929:with
6573:is a
6549:is a
6520:is a
6125:Gibbs
5977:of a
5919:joule
4340:Joule
3660:phase
3633:Many
3556:ÏÏÎżÏÎź
3549:áŒÏÎłÎżÎœ
3494:over
3426:ÏÏÎżÏÎź
3413:state
3153:is a
3068:Chaos
2596:Bragg
2591:Raman
2561:Salam
2531:Higgs
2521:Nambu
2471:Dirac
2461:Gödel
2441:Dyson
2426:Fermi
2416:Pauli
2356:Onnes
2351:Soddy
2326:Curie
2103:Light
2063:Space
1635:Other
1602:Stahl
1557:Lewis
1547:Joule
1537:Gibbs
1532:Duhem
225:State
185:Third
175:First
18109:and
17831:and
17487:Asia
17241:Wind
17182:Coal
17154:Work
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17098:Fuel
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1879:)
1876:t
1873:(
1868:n
1859:|
1852:t
1849:d
1845:d
1837:i
1834:=
1828:)
1825:t
1822:(
1817:n
1808:|
1798:H
1767:e
1760:t
1753:v
1701:e
1694:t
1687:v
1214:S
1211:T
1205:H
1202:=
1199:)
1196:p
1193:,
1190:T
1187:(
1184:G
1159:S
1156:T
1150:U
1147:=
1144:)
1141:V
1138:,
1135:T
1132:(
1129:A
1104:V
1101:p
1098:+
1095:U
1092:=
1089:)
1086:p
1083:,
1080:S
1077:(
1074:H
1049:)
1046:V
1043:,
1040:S
1037:(
1034:U
911:T
887:V
864:V
840:1
815:=
779:p
755:V
732:V
708:1
680:=
644:T
620:N
597:S
573:T
548:=
545:c
468:)
58:S
38:.
31:.
24:.
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