On the second law of thermodynamics

The second law of thermodynamics has two distinct aspects to its foundations. The first concerns the question of why entropy goes up in the future, and the second, of why it goes down in the past. Statistical physicists tend to be more concerned with the first question and with careful considerations of definition and mathematical detail. The second question is of quite a different nature; it leads into areas of cosmology and quantum gravity, where the mathematical and physical issues are ill understood.     

Memory systems,computation, and the second law of thermodynamics

A memory is a physical system for transferring information from one moment in time to another, where that information concerns something external to the system itself. This paper argues on information-theoretic and statistical mechanical grounds that useful memories must be of one of two types, exemplified by memory in abstract computer programs and by memory in photographs. Photograph-type memories work by exploiting a collapse of state space flow to an attractor state. (This attractor state is the initialized state of the memory.) The central assumption of the theory of reversible computation tells us that inany such collapsing, regardless of whether the collapsing proceeds from the past to the future or vice versa, the collapsing must increase the entropy of the system. In concert with the second law, this establishes the logical necessity of the empirical observation that photograph-type memories are temporally asymmetric (they can tell us about the past but not about the future). Under the assumption that human memory is a photograph-type memory, this result also explains why we humans can remember only our past and not our future. In contrast to photograph-type memories, computer-type memories do not require any initialization, and therefore are not directly affected by the second law. As a result, computer memories can be of the future as easily as of the past, even if the program running on the computer is logically irreversible. This is entirely in accord with the well-known temporal reversibility of the process of computation. This paper ends by arguing that the asymmetry of the psychological arrow of time is a direct consequence of the asymmetry of human memory. With the rest of this paper, this explains, explicitly and rigorously, why the psychological and thermodynamic arrows of time are correlated with one another.     

Universal thermodynamics in different gravity theories: Conditions for generalized second law of thermodynamics and thermodynamical equilibrium on the horizons

The present work deals with a detailed study of universal thermodynamics in different modified gravity theories. The validity of the generalized second law of thermodynamics (GSLT) and thermodynamical equilibrium (TE) of the Universe bounded by a horizon (apparent/event) in f(R)$f\left(R\right)$-gravity, Einstein–Gauss–Bonnet gravity, RS-II brane scenario and DGP brane model has been investigated. In the perspective of recent observational evidences, the matter in the Universe is chosen as interacting holographic dark energy model. The entropy on the horizons is evaluated from the validity of the unified first law and as a result there is a correction (in integral form) to the usual Bekenstein entropy. The other thermodynamical parameter namely temperature on the horizon is chosen as the recently introduced corrected Hawking temperature. The above thermodynamical analysis is done for homogeneous and isotropic flat FLRW model of the Universe. The restrictions for the validity of GSLT and the TE are presented in tabular form for each gravity theory. Finally, due to complicated expressions, the validity of GSLT and TE are also examined from graphical representation, using three Planck data sets.     

Some remarks on the second law of thermodynamics

We show that the existence of a temperature scale implies the existence of the absolute temperature and the entropy. The consequences for the structure of thermodynamics are discussed.     

Quantum Brownian motion and the second law of thermodynamics

We consider a single harmonic oscillator coupled to a bath at zero temperature. As is well-known, the oscillator then has a higher average energy than that given by its ground state. Here we show analytically that for a damping model with arbitrarily discrete distribution of bath modes and damping models with continuous distributions of bath modes with cut-off frequencies, this excess energy is less than the work needed to couple the system to the bath, therefore, the quantum second law is not violated. On the other hand, the second law may be violated for bath modes without cut-off frequencies, which are, however, physically unrealistic models. An erratum to this article is available at .     

热力学第二定律的非对称性

热力学第二定律揭示了自然界中存在着的非对称性。     

The physics and mathematics of the second law of thermodynamics

     

11.

Maxwell’s demon and the second law of thermodynamics     

Richard L. Liboff 《Foundations of Physics Letters》1997,10(1):89-92

An idealized, two-dimensional Maxwell demon is described which incorporates an irreversible process. The vertex of the device acts as a purely mechanical ‘trap door’. This idealized mechanism is found to generate a violation of the second law of thermodynamics. These results indicate that the second law of thermodynamics is not valid in general for idealized, irreversible systems.     

12.

Validity of the second law in nonextensive quantum thermodynamics     

Abe S  Rajagopal AK 《Physical review letters》2003,91(12):120601

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range q in (0, 2]. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists no upper bound of q for validity of the second law in classical theory.     

13.

Can inflation explain the second law of thermodynamics?     

Don N. Page 《International Journal of Theoretical Physics》1984,23(8):725-733

The inflationary model of the universe can explain several of the cosmological conundra that are mysteries in the standard hot big bang model. Paul Davies has suggested that inflation can also explain the second law of thermodynamics, which describes the time asymmetry of the universe. Here I note several difficulties with this suggestion, showing how the present inflationary models must assume the arrow of time rather than explaining it. If the second law is formulated as a consequence of the hypothesis that there were no long-range spatial correlations in the initial state of the universe, it is shown how some of the cosmological conundra might be explained even without inflation. But if the ultimate explanation is to include inflation, three, essential elements remain to be demonstrated which I list.     

14.

On the second law of thermodynamics I. General framework     

M. šilhavý 《Czechoslovak Journal of Physics》1982,32(9):987-1010

In this paper a general framework for discussing the classical statements of the second law of thermodynamics is developed. The thermodynamic systems with which the theory deals need not obey the first law and can undergo general (not necessarily quasi-static) processes. By using the formalism of heat distribution measures introduced in previous papers of the author, the classical verbal statements are converted into meaningful mathematical conditions. These conditions can be put into a general form which is the same for all the classical statements. The main result of the paper is an abstract theorem which shows that the general condition leads to one or two inequalities for cyclic processes. In the subsequent part of the paper the abstract theorem is applied to the specific conditions corresponding to the classical statements of the second law. The number of the corresponding inequalities depends on the condition in question, but in each case these inequalities are generalization of the Clausius inequality to which they reduce if the first law holds. By comparing the inequalities corresponding to various statements of the second law also the relations among the statements are established in the second part of the paper.I wish to thank Dr. Jan Kratochvil, DrSc for a number of helpful suggestions concerning a previous draft of the paper.     

15.

Violation of the second law of thermodynamics in the quantum microworld     

V. pek  J. Bok 《Physica A》2001,290(3-4)

One of the previously reported linear models of open quantum systems (interacting with a single thermal bath but otherwise not aided from outside) endowed with the faculty of spontaneous self-organization challenging standard thermodynamics is reconstructed here. It is then able to produce, in a cyclic manner, a useful (this time mechanical) work at the cost of just thermal energy in the bath whose quanta get properly in-phased. This means perpetuum mobile of the second kind explicitly violating the second law in its Thomson formulation. No approximations can be made responsible for the effect as a special scaling procedure is used that makes the chosen kinetic theory exact. The effect is purely quantum and disappears in the classical limit.     

16.

Generalized second law of thermodynamics in quintom dominated universe     

M.R. Setare 《Physics letters. [Part B]》2006

In this Letter we will investigate the validity of the generalized second law of thermodynamics for the quintom model of dark energy. Reviewing briefly the quintom scenario of dark energy, we will study the conditions of validity of the generalized second law of thermodynamics in three cases: quintessence dominated, phantom dominated and transition from quintessence to phantom will be discussed.     

17.

The second law of thermodynamics and the limiting capabilities of heat engines     

A. M. Tsirlin 《Technical Physics》1999,44(1):129-131

     

18.

Nonequilibrium thermodynamics at the microscale: Work relations and the second law     

Eliran Boksenbojm  Christopher Jarzynski 《Physica A》2010,389(20):4406-883

For macroscopic systems, the second law of thermodynamics establishes an inequality between the amount of work performed on a system in contact with a thermal reservoir, and the change in its free energy. For microscopic systems, this result must be considered statistically, as fluctuations around average behavior become substantial. In recent years it has become recognized that these fluctuations satisfy a number of strong and unexpected relations, which remain valid even when the system is driven far from equilibrium. We discuss these relations, and consider what they reveal about the second law of thermodynamics and the nature of irreversibility at the microscale.     

19.

Quantum approach to a derivation of the second law of thermodynamics     

Gemmer J  Otte A  Mahler G 《Physical review letters》2001,86(10):1927-1930

We reinterpret the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas subsystem" under consideration and its environment ("container"). The time average of a purity measure is found to equal the average over the respective path in Hilbert space. We then show that for typical (degenerate or nondegenerate) thermodynamical systems almost all states within the allowed region of Hilbert space have a local von Neumann entropy S close to the maximum and a purity P close to its minimum, respectively. Typically, thermodynamical systems should obey the second law.     

20.

A general information theoretical proof for the second law of thermodynamics     

QiRen Zhang 《中国科学G辑(英文版)》2008,51(7):813-816

It is shown that the conservation and the non-additivity of the information, together with the additivity of the entropy, make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the non-additivity of information is also true in other fields in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive. Supported by the National Natural Science Foundation of China (Grant No. 10305001)     

Maxwell’s demon and the second law of thermodynamics

An idealized, two-dimensional Maxwell demon is described which incorporates an irreversible process. The vertex of the device acts as a purely mechanical ‘trap door’. This idealized mechanism is found to generate a violation of the second law of thermodynamics. These results indicate that the second law of thermodynamics is not valid in general for idealized, irreversible systems.     

Validity of the second law in nonextensive quantum thermodynamics

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range q in (0, 2]. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists no upper bound of q for validity of the second law in classical theory.     

Can inflation explain the second law of thermodynamics?

The inflationary model of the universe can explain several of the cosmological conundra that are mysteries in the standard hot big bang model. Paul Davies has suggested that inflation can also explain the second law of thermodynamics, which describes the time asymmetry of the universe. Here I note several difficulties with this suggestion, showing how the present inflationary models must assume the arrow of time rather than explaining it. If the second law is formulated as a consequence of the hypothesis that there were no long-range spatial correlations in the initial state of the universe, it is shown how some of the cosmological conundra might be explained even without inflation. But if the ultimate explanation is to include inflation, three, essential elements remain to be demonstrated which I list.     

On the second law of thermodynamics I. General framework

In this paper a general framework for discussing the classical statements of the second law of thermodynamics is developed. The thermodynamic systems with which the theory deals need not obey the first law and can undergo general (not necessarily quasi-static) processes. By using the formalism of heat distribution measures introduced in previous papers of the author, the classical verbal statements are converted into meaningful mathematical conditions. These conditions can be put into a general form which is the same for all the classical statements. The main result of the paper is an abstract theorem which shows that the general condition leads to one or two inequalities for cyclic processes. In the subsequent part of the paper the abstract theorem is applied to the specific conditions corresponding to the classical statements of the second law. The number of the corresponding inequalities depends on the condition in question, but in each case these inequalities are generalization of the Clausius inequality to which they reduce if the first law holds. By comparing the inequalities corresponding to various statements of the second law also the relations among the statements are established in the second part of the paper.I wish to thank Dr. Jan Kratochvil, DrSc for a number of helpful suggestions concerning a previous draft of the paper.     

Violation of the second law of thermodynamics in the quantum microworld

One of the previously reported linear models of open quantum systems (interacting with a single thermal bath but otherwise not aided from outside) endowed with the faculty of spontaneous self-organization challenging standard thermodynamics is reconstructed here. It is then able to produce, in a cyclic manner, a useful (this time mechanical) work at the cost of just thermal energy in the bath whose quanta get properly in-phased. This means perpetuum mobile of the second kind explicitly violating the second law in its Thomson formulation. No approximations can be made responsible for the effect as a special scaling procedure is used that makes the chosen kinetic theory exact. The effect is purely quantum and disappears in the classical limit.     

Generalized second law of thermodynamics in quintom dominated universe

In this Letter we will investigate the validity of the generalized second law of thermodynamics for the quintom model of dark energy. Reviewing briefly the quintom scenario of dark energy, we will study the conditions of validity of the generalized second law of thermodynamics in three cases: quintessence dominated, phantom dominated and transition from quintessence to phantom will be discussed.     

Nonequilibrium thermodynamics at the microscale: Work relations and the second law

For macroscopic systems, the second law of thermodynamics establishes an inequality between the amount of work performed on a system in contact with a thermal reservoir, and the change in its free energy. For microscopic systems, this result must be considered statistically, as fluctuations around average behavior become substantial. In recent years it has become recognized that these fluctuations satisfy a number of strong and unexpected relations, which remain valid even when the system is driven far from equilibrium. We discuss these relations, and consider what they reveal about the second law of thermodynamics and the nature of irreversibility at the microscale.     

Quantum approach to a derivation of the second law of thermodynamics

We reinterpret the microcanonical conditions in the quantum domain as constraints for the interaction of the "gas subsystem" under consideration and its environment ("container"). The time average of a purity measure is found to equal the average over the respective path in Hilbert space. We then show that for typical (degenerate or nondegenerate) thermodynamical systems almost all states within the allowed region of Hilbert space have a local von Neumann entropy S close to the maximum and a purity P close to its minimum, respectively. Typically, thermodynamical systems should obey the second law.     

A general information theoretical proof for the second law of thermodynamics

It is shown that the conservation and the non-additivity of the information, together with the additivity of the entropy, make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the non-additivity of information is also true in other fields in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true not only in quantum and classical physics but also in other processes in which the information is conservative and non-additive. Supported by the National Natural Science Foundation of China (Grant No. 10305001)