Thermodynamical Aspects of Modified Holographic Dark Energy Model

We investigate the unified first law and the generalized second law in a modified holographic dark energy model. The thermodynamical analysis on the apparent horizon can work and the corresponding entropy formula is extracted from the systematic algorithm. The entropy correction term depends on the extra-dimension number of the brane as expected, but the interplay between the correction term and the extra dimensions is more complicated. With the unified first law of thermodynamics well-founded, the generalized second law of thermodynamics is discussed and it is found that the second law can be violated in certain circumstances. Particularly, if the number of the extra dimensions is larger than one, the generalized law of thermodynamics is always satisfied; otherwise, the validity of the second law can only be guaranteed with the Hubble radius greatly smaller than the crossover scale r_c of the 5-dimensional DGP model.     

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.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann-Robertson-Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Thermodynamics in Higher Dimensional Vaidya Space-Time

In this work, we have considered the Vaidya spacetime in null radiating fluid with perfect fluid in higher dimension and have found the solution for barotropic fluid. We have shown that the Einstein’s field equations can be obtained from Unified first law i.e., field equations and unified first law are equivalent. The first law of thermodynamics has also been constructed by Unified first law. From this, the variation of entropy function has been derived on the horizon. The variation of entropy function inside the horizon has been derived using Gibb’s law of thermodynamics. So the total variation of entropy function has been constructed at apparent and event horizons both. If we do not assume the first law, then the entropy on the both horizons can be considered by area law and the variation of total entropy has been found at both the horizons. Also the validity of generalized second law (GSL) of thermodynamics has been examined at both apparent and event horizons by using the first law and the area law separately. When we use first law of thermodynamics and Bekenstein-Hawking area law of thermodynamics, the GSL for apparent horizon in any dimensions are satisfied, but the GSL for event horizon can not be satisfied in any dimensions.     

The Second Law of Thermodynamics in a Quantum Heat Engine Model

The second law of thermodynamics has been proven by many facts in classical world. Is there any new property of it in quantum world? In this paper, we calculate the change of entropy in T.D. Kieu's model for quantum heat engine (QHE) and prove the broad validity of the second law of thermodynamics. It is shown that the entropy of the quantum heat engine neither decreases in a whole cycle, nor decreases in either stage of the cycle. The second law of thermodynamics still holds in this QHE model. Moreover, although the modified quantum heat engine is capable of extracting more work, its efficiency does not improve at all. It is neither beyond the efficiency of T.D. Kieu's initial model, nor greater than the reversible Carnot efficiency.     

Effect of arbitrary matter-geometry coupling on thermodynamics in f(R) theories of gravity

In this paper, the thermodynamics of the Friedmann–Lemaître–Robertson–Walker universe have been explored in f(R) theories of gravity with arbitrary matter-geometry coupling. The equivalence between the modified Friedmann equations with any spatial curvature and the first law of thermodynamics is confirmed, where the assumption of the entropy plays a crucial role. Then laws of thermodynamics in our considering case are obtained. They can reduce to the ones given in Einstein’s general theory of relativity under certain conditions. Moreover, a particular model is investigated through the obtained generalized second law of thermodynamics with observational results of cosmographic parameters.     

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.     

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.     

Maxwell’s demon and the management of ignorance in stochastic thermodynamics

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics, the demon fails because on average, more work is performed upfront in making a measurement than can be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

Generalized second law of thermodynamics in Gauss–Bonnet braneworld

We investigate the validity the generalized second law of thermodynamics in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. Employing the derived entropy expression associated with the apparent horizon, we examine the time evolution of the total entropy, including the derived entropy of the apparent horizon and the entropy of the matter fields inside the apparent horizon. We show that the generalized second law of thermodynamics is fulfilled on the 3-brane embedded in the 5D spacetime with curvature corrections.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi(LTB) cosmology supported by a perfect Suid source.This model is the natural generalization of the Sat Friedmann-Robertson-Walker(FRW) universe,and describes an inhomogeneous universe with spherical symmetry.After reviewing some basic equations in the parabolic LTB cosmology,we obtain a relation for the deceleration parameter in this model.We also obtain a condition for which the universe undergoes an accelerating phase at the present time.We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology.We find out that in LTB model of cosmology,the apparent horizon's entropy could be feeded by a term,which incorporates the effects of the inhomogeneity.We consider this result and get a relation for the total entropy evolution,which is used to examine the generalized second law of thermodynamics for an accelerating universe.We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Entropies of the various components of the universe

In this study, we investigate the entropies of photons, ideal gas-like dust (baryonic matter), and a special kind of dark energy in the context of cosmology. When these components expand freely with the universe, we calculate the entropy and specific entropy of each component from the perspective of statistics. Under specific assumptions and conditions, the entropies of these components can satisfy the second law of thermodynamics independently. Our calculations show that the specific entropy of matter cannot be a constant during the expansion of the universe, except for photons. When these components interact with the space-time background, particle production (annihilation) can occur. We study the influence of the interaction on the entropies of these components and obtain the conditions guaranteeing that the entropy of each component satisfies the second law of thermodynamics.     

Interacting three fluid system and thermodynamics of the universe bounded by the event horizon

The work deals with the thermodynamics of the universe bounded by the event horizon. The matter in the universe has three constituents namely dark energy, dark matter and radiation in nature and interaction between then is assumed. The variation of entropy of the surface of the horizon is obtained from unified first law while matter entropy variation is calculated from the Gibbss’ law. Finally, validity of the generalized second law of thermodynamics is examined and conclusions are written point wise.     

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.     

熵定理的新讲法

改进费米方法后，无须卡诺定理，即可由热力学第二定律开尔文表述直接推导克劳修斯等式、不等式，从而得到熵和熵增加原理．     

Information Erasure and the Generalized Second Law of Black Hole Thermodynamics

We consider the generalized second law of black hole thermodynamics in the light of quantum information theory, in particular information erasure and Landauer’s principle (namely, that erasure of information produces at least the equivalent amount of entropy). A small quantum system outside a black hole in the Hartle-Hawking state is studied, and the quantum system comes into thermal equilibrium with the radiation surrounding the black hole. For this scenario, we present a simple proof of the generalized second law based on quantum relative entropy. We then analyze the corresponding information erasure process, and confirm our proof of the generalized second law by applying Landauer’s principle.     

Extensivity and the thermodynamic limit: Why size really does matter

The thermodynamic limit and extensivity are central concepts in thermodynamics. In this paper, these are critically examined in light of systems for which they appear inadequate. It is found that their limitations lead to counterintuitive thermodynamic results involving heat flow, phase separations, thermostatistics of gravitating systems and the conversion efficiency of heat into work. Ultimately, these limitations are shown to bear on the utility of entropy and the universality of the second law of thermodynamics.     

Thermal Relativity

The group G of general coordinate transformations on the thermodynamic configuration space E spanned by all the extensive variables keeps the first law of thermodynamics invariant. One can introduce a metric with Lorentzian signature on the space E, with the corresponding line element also being invariant under the action of G. This line element is identified as the square of the proper entropy. Thus the second law of thermodynamics is also formulated invariantly and this lays down the foundation for the principle of thermal relativity.     

满足热力学第三定律的修正的黑洞的熵公式

认为黑洞的熵正比于视界面积的熵公式S=A/4不能满足热力学第三定律,提出了新的熵公式,它既能满足热力学第三定律,又能推出黑洞的温度的表达式. 关键词： 黑洞 熵 热力学第三定律