Hawking radiation as tunneling and the unified first law of thermodynamics at the apparent horizon of the FRW universe

Relations between the tunneling rate FRW universe are investigated. The namics in such a dynamical system. first law of thermodynamics through and the unified first law of thermodynamics at the apparent horizon of the tunneling rate arises as a consequence of the unified first law of thermodyAnalysis shows how the tunneling is intimately connected with the unified the principle of conservation of energy.     

Information conservation, entropy increase and statistical irreversibility for an isolated system

We consider statistical irreversibility and its compatibility with reversible dynamics. The role played by the observation is analyzed in detail. It makes our previous proof for the second law of thermodynamics clearer. On this basis, we emphasize the importance and wide applicability of the second law of thermodynamics. A new form of physics with this law substituted by the principle of information conservation is suggested. By the way, we also solve the paradox of Schrödinger cat, and show that the universe will not go to the so-called heat death spontaneously.     

Thermodynamics of Universe with Time Varying Cosmological Term

The FRW-type cosmologies with time varying cosmological term is discussed within the frame work of a thermodynamic context. If at some cosmological time, the cosmological term begins increasing again, as presently observed, expansion will accelerate and matter and/or radiation will be transformed back into dark energy. It is shown that such accelerated expansion is a route towards a new kind of gravitational singular state, characterized by an empty, conformally transitive spacetime in which all energy is dark. We investigate whether dynamic dark energy cosmologies are compatible with the second law of thermodynamics. We examine also the total entropy evolution with time. We observed that the dynamic dark energy cosmology is less restricted with second law of thermodynamics. Some physical implications of these solutions are briefly discussed.     

Elementary Concepts and Fundamental Laws of the Theory of Heat

The elementary concepts and fundamental laws concerning the science of heat are examined from the point of view of its development with special attention to its theoretical structure. The development is divided into four periods, each one characterized by the concept that was attributed to heat. The transition from one to the next period was marked by the emergence of new concepts and new laws, and by singular events. We point out that thermodynamics, as it emerged, is founded on the elementary concepts of temperature and adiabatic wall, and on the fundamental laws: Mayer-Joule principle, or law of conservation of energy; Carnot principle, which leads to the definition of entropy; and the Clausius principle, or law of increase in entropy.     

Electron self-organization in electronic devices in the light of principles of mechanics and thermodynamics

The principle of least action is extended for many-particle systems. The equivalency of basic energy relationships of mechanics and thermodynamics is demonstrated. It is shown that crystallization of solutions in thermodynamics and self-organization of electronic structures in electronic devices obey the same laws. The definition of thermodynamic information is refined.     

Thermodynamical considerations on the quantum efficiency of anti-stokes co-operative luminescence

It is shown that the second law of thermodynamics imposes an additional restriction on the quantum efficiency of the anti-Stokes co-operative luminescence besides the energy conservation law. This restriction is very severe for the excitation by ordinary light, while it can be neglected at very high intensities of the exciting radiation (e.g. laser excitation).     

Intensive variables in the framework of the non-extensive thermostatistics

By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner consistent with the thermostatistics structure of the theory. We show that the definitions of these quantities are sensitive to the composition law of entropy and internal energy governing the system. In this way, we can clarify some questions raised about the possible introduction of intensive variables in the context of non-extensive statistical mechanics.     

On the universality of thermodynamics' Legendre transform structure

It is shown that the Legendre transform structure of thermodynamics does not depend upon the functional form of the entropy. It is a just a necessary consequence of Jaynes' maximum entropy principle. Moreover, in the important special case of the canonical ensemble, the Legendre transform structure of thermodynamics is shown to be independent of the functional form of the mean energy constraint as well.     

Thermodynamics of Lema$$\hat{i}$$ tre−Tolman−Bondi Model

Here we consider our universe as inhomogeneous spherically symmetric Lema [^(i)]{\hat{i}} tre−Tolman−Bondi Model and analyze the thermodynamics of this model of the universe. The trapping horizon is calculated and is found to coincide with the apparent horizon. The Einstein field equations are shown to be equivalent with the unified first law of thermodynamics. Finally assuming the first law of thermodynamics validity of the generalized second law of thermodynamics is examined at the apparent horizon for the perfect fluid and at the event horizon for holographic dark energy.     

Two long-standing problems in Tsallis’ statistics

On the basis of Tsallis’ entropy and the joint probability factorization condition, two controversial problems existing in Tsallis’ statistics are investigated, where one is whether energy is extensive or not and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not. The results obtained show clearly that like entropy, energy is also nonextensive in Tsallis’ statistics, and that the zeroth law of thermodynamics has been implicitly used in Tsallis’ statistics since 1988. Moreover, it is expounded that the standard energy additivity rule adopted by a great number of researchers is not suitable in Tsallis’ statistics, because its corollary is in contradiction with the zeroth law of thermodynamics.     

Mathematical Formalism of Nonequilibrium Thermodynamics for Nonlinear Chemical Reaction Systems with General Rate Law

This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs’ macroscopic chemical thermodynamics under G. N. Lewis’ kinetic law of entire equilibrium (detailed balance in nonlinear chemical kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.     

On the determination of the Debye temperature from experimental data

It is shown that the Debye temperature as a function of temperature must satisfy certain equations in order for the thermodynamic functions calculated in terms of the Debye temperature to satisfy both the third law of thermodynamics and the law of equipartition of energy. A general expression for the Θ(T) function satisfying these thermodynamic laws is found.     

Fundamental functions in equilibrium thermodynamics

In the standard presentations of the principles of Gibbsian equilibrium thermodynamics one can find several gaps in the logic. For a subject that is as widely used as equilibrium thermodynamics, it is of interest to clear up such questions of mathematical rigor. In this paper it is shown that using convex analysis one can give a mathematically rigorous treatment of several basic aspects of equilibrium thermodynamics. On the basis of a fundamental convexity property implied by the second law, the following topics are discussed: thermodynamic stability, transformed fundamental functions (such as the Gibbs free energy), and the existence and uniqueness of possible final equilibrium states of closed composite thermodynamic systems. It is shown that a standard mathematical characterization of thermodynamic stability (involving a positive definiteness property) is sufficient but in fact not necessary for the physically superior convexity characterization of thermodynamic stability. Furthermore, it is found that functions such as the Gibbs free energy can be rigorously and globally defined using convex conjugation instead of Legendre transformation. Another result desribed in this paper is that equilibrium thermodynamics cannot always uniquely predict possible final equilibrium states of closed composite thermodynamic systems.     

Kaluza–Klein cosmology with modified holographic dark energy

We investigate the compact Kaluza–Klein cosmology in which modified holographic dark energy is interacting with dark matter. Using this scenario, we evaluate equation of state parameter as well as equation of evolution of the modified holographic dark energy. Further, it is shown that the generalized second law of thermodynamics holds without any constraint.     

Insights into the Second Law of Thermodynamics from Anisotropic Gas-Surface Interactions

Thermodynamic implications of anisotropic gas-surface interactions in a closed molecular flow cavity are examined. Anisotropy at the microscopic scale, such as might be caused by reduced-dimensionality surfaces, is shown to lead to reversibility at the macroscopic scale. The possibility of a self-sustaining nonequilibrium stationary state induced by surface anisotropy is demonstrated that simultaneously satisfies flux balance, conservation of momentum, and conservation of energy. Conversely, it is also shown that the second law of thermodynamics prohibits anisotropic gas-surface interactions in “equilibrium”, even for reduced dimensionality surfaces. This is particularly startling because reduced dimensionality surfaces are known to exhibit a plethora of anisotropic properties. That gas-surface interactions would be excluded from these anisotropic properties is completely counterintuitive from a causality perspective. These results provide intriguing insights into the second law of thermodynamics and its relation to gas-surface interaction physics. Sandia National Laboratories is the author’s employer, but is not officially affiliated with this work.     

Thermodynamics in the statistical theory of a crystal

The thermodynamics of a crystal is developed on the basis of the Vlasov equation. From this equation a system of equations is derived for the Fourier coefficients of the density. The internal energy and stress tensor are found. It is shown that the results obtained satisfy the second law of thermodynamics and the entropy is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 85–88, December, 1978.     

Some variational principles in electroelastic media under finite deformation

It is proposed that the universal thermodynamic energy variational principle is included in the first law of thermodynamics. Some variational principles in the electroelastic media under finite deformation are derived from this universal thermodynamic variational principle. It is suggested that in the general electroelastic analysis the environment should be considered together with the discussed electroelastic medium. For the variational principle of nonlinear electroelastic media the variation of the electric potential is coupled with the virtual displacement, and the variation of the initial volume should be considered. The Maxwell stress in the initial configuration is naturally derived from this variational principle and it is unique in the second order precision. Supported by the National Natural Science Foundation of China (Grant No. 10472069)     

The Third Law of Quantum Thermodynamics in the Presence of Anomalous Couplings

The quantum thermodynamic functions of a harmonic oscillator coupled to a heat bath through velocity-dependent coupling are obtained analytically. It is shown that both the free energy and the entropy decay fast with the temperature in relation to that of the usual coupling from. This implies that the velocity-dependent coupling helps to ensure the third law of thermodynamics.     

Thermodynamics of the Apparent Horizon in FRW Universe with Massive Gravity

Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation δQ=T dS, where the heat flow δQ is the energy-supply of pure matter projecting on the vector ζ tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/2πrA, the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit H_c→0, which recovers the Minkowski reference metric solution in the flat case, the generalized second law of thermodynamics holds if α₃+4α₄<0. Without this condition, even for the simplest model of dRGT massive cosmology with α₃=α₄=0, the generalized second law of thermodynamics could be violated.     

Incomplete nonextensive statistics and the zeroth law of thermodynamics

On the basis of the entropy of incomplete statistics (IS) and the joint probability factorization condition, two controversial problems existing in IS are investigated: one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.