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.     

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.     

Life,gravity and the second law of thermodynamics

We review the cosmic evolution of entropy and the gravitational origin of the free energy required by life. All dissipative structures in the universe including all forms of life, owe their existence to the fact that the universe started in a low entropy state and has not yet reached equilibrium. The low initial entropy was due to the low gravitational entropy of the nearly homogeneously distributed matter and has, through gravitational collapse, evolved gradients in density, temperature, pressure and chemistry. These gradients, when steep enough, give rise to far from equilibrium dissipative structures (e.g., galaxies, stars, black holes, hurricanes and life) which emerge spontaneously to hasten the destruction of the gradients which spawned them. This represents a paradigm shift from “we eat food” to “food has produced us to eat it”.     

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 .     

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.     

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。     

热力学第二定律理论体系的讨论

热力学第二定律原有的两个理论体系都有明显的不足之处,为此,综全各种方法的优点,利用我们提出的简单物质可逆补热循环以及微分方程基本理论,简单明确地直接由热力学第二定律的开尔文表述推导克劳修斯等式、不等式,在推导过程中自然地引出绝对温度,得到热力学熵和增加原理,从而建立起热力学第二定律的新理论体系。     

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)     

The physics and mathematics of the second law of thermodynamics

     

14.

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.     

15.

Unification of small and large time scales for biological evolution: deviations from power law     

Chowdhury D  Stauffer D  Kunwar A 《Physical review letters》2003,90(6):068101

We develop a unified model that describes both "micro" and "macro" evolutions within a single theoretical framework. The ecosystem is described as a dynamic network; the population dynamics at each node of this network describes the "microevolution" over ecological time scales (i.e., birth, ageing, and natural death of individual organisms), while the appearance of new nodes, the slow changes of the links, and the disappearance of existing nodes accounts for the "macroevolution" over geological time scales (i.e., the origination, evolution, and extinction of species). In contrast to several earlier claims in the literature, we observe strong deviations from power law in the regime of long lifetimes.     

16.

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.     

17.

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.     

18.

On the second law of thermodynamics II. Inequalities for cyclic processes     

M. Šilhavý 《Czechoslovak Journal of Physics》1982,32(10):1073-1099

Consequences of and relations among the classical statements of the second law of thermodynamics are derived for non-equilibrium thermodynamic systems not necessarily satisfying the first law. It is shown that each classical version of the second law implies one or two inequalities for cyclic processes which yield the Clausius inequality for cyclic processes if the first law holds. The inequalities for cyclic processes are derived by means of a general theorem stated and proved in the first part.The author wishes to express his deep thanks to Dr. Jan Kratochvíl for reading a previous draught of the paper and for discussing the topics dealt with in it.     

19.

Inequalities generalizing the second law of thermodynamics for transitions between nonstationary states     

Verley G  Chétrite R  Lacoste D 《Physical review letters》2012,108(12):120601

We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and nonadiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law-like inequalities for transitions between nonstationary states.     

20.

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.     

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.     

Unification of small and large time scales for biological evolution: deviations from power law

We develop a unified model that describes both "micro" and "macro" evolutions within a single theoretical framework. The ecosystem is described as a dynamic network; the population dynamics at each node of this network describes the "microevolution" over ecological time scales (i.e., birth, ageing, and natural death of individual organisms), while the appearance of new nodes, the slow changes of the links, and the disappearance of existing nodes accounts for the "macroevolution" over geological time scales (i.e., the origination, evolution, and extinction of species). In contrast to several earlier claims in the literature, we observe strong deviations from power law in the regime of long lifetimes.     

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.     

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.     

On the second law of thermodynamics II. Inequalities for cyclic processes

Consequences of and relations among the classical statements of the second law of thermodynamics are derived for non-equilibrium thermodynamic systems not necessarily satisfying the first law. It is shown that each classical version of the second law implies one or two inequalities for cyclic processes which yield the Clausius inequality for cyclic processes if the first law holds. The inequalities for cyclic processes are derived by means of a general theorem stated and proved in the first part.The author wishes to express his deep thanks to Dr. Jan Kratochvíl for reading a previous draught of the paper and for discussing the topics dealt with in it.     

Inequalities generalizing the second law of thermodynamics for transitions between nonstationary states

We discuss the consequences of a variant of the Hatano-Sasa relation in which a nonstationary distribution is used in place of the usual stationary one. We first show that this nonstationary distribution is related to a difference of traffic between the direct and dual dynamics. With this formalism, we extend the definition of the adiabatic and nonadiabatic entropies introduced by M. Esposito and C. Van den Broeck in Phys. Rev. Lett. 104, 090601 (2010) for the stationary case. We also obtain interesting second-law-like inequalities for transitions between nonstationary states.     

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.