Thermodynamics of general scalar-tensor theory with non-minimally derivative coupling

With the usual definitions for the entropy and the temperature associated with the apparent horizon, we discuss the first law of the thermodynamics on the apparent in the general scalar-tensor theory of gravity with the kinetic term of the scalar field non-minimally coupling to Einstein tensor. We show the equivalence between the first law of thermodynamics on the apparent horizon and Friedmann equation for the general models, by using a mass-like function which is equal to the Misner-Sharp mass on the apparent horizon. The results further support the universal relationship between the first law of thermodynamics and Friedmann equation.     

Macroscopic Form of the First Law of Thermodynamics for an Adibatically Evolving <Emphasis Type="Italic">Non-singular</Emphasis> Self-gravitating Fluid

We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve proper volume element rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation as well as particle number conservation equation. It is also emphasized that we are considering here a non-singular fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum gravity which apparently suggests thermodynamical properties even for a (singular) black hole. Having made such a clarification, we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified that such a global first law of thermodynamics, for a non-singular fluid, has not been formulated earlier.     

The second law of thermodynamics revisited I. The absolute zero of potential and the general expression for the efficiency of universal reversible cycle

The fundamental equation of thermodynamics expresses the internal energy of a system as a function of all the extensive parameters of the system. The differential form of this equation is referred to as the Gibbs equation. We have integrated this equation and have used it to derive an expression characterising the efficiency of a system for any kind of cyclical process by which work is produced. This system has access to two reservoirs at low and high thermodynamics potential respectively. It is claimed that all thermodynamic potentials (temprature, chemical potential, hydrostatic pressure, electric potential, etc) can have an absolute value of zero which we defined as the value of the potential in the lower reservoir when the efficiency of the cycle is 1. It is also shown that the classical Carnot machine, in which heat is converted into mechanical work, is an example of the general expression.     

Thermodynamics on the apparent horizon in generalized gravity theories

We present a general procedure to construct the first law of thermodynamics on the apparent horizon and illustrate its validity by examining it in some extended gravity theories. Applying this procedure, we can describe the thermodynamics on the apparent horizon in Randall–Sundrum braneworld imbedded in a nontrivial bulk. We discuss the mass-like function which was used to link Friedmann equation to the first law of thermodynamics and obtain its special case which gives the generalized Misner–Sharp mass in Lovelock gravity.     

Friedmann equations and thermodynamics of apparent horizons

With the help of a masslike function which has a dimension of energy and is equal to the Misner-Sharp mass at the apparent horizon, we show that the first law of thermodynamics of the apparent horizon dE=T(A)dS(A) can be derived from the Friedmann equation in various theories of gravity, including the Einstein, Lovelock, nonlinear, and scalar-tensor theories. This result strongly suggests that the relationship between the first law of thermodynamics of the apparent horizon and the Friedmann equation is not just a simple coincidence, but rather a more profound physical connection.     

On an ideal gas related to the law of corresponding states

By an “ideal gas” we mean a gas which formally does not depend on the form of the interaction between the particles. We construct the thermodynamics (the equation of state) of such a gas, and this thermodynamics depends on three parameters corresponding to the Zeno-line and to the value of the compressibility factor Z at the critical point (a three-parameter family of three-dimensional Lagrangian manifolds).     

Viscous Cosmology and Thermodynamics of Apparent Horizon in Modified Friedman-Robertson-Walkers Universe

In this paper, we write modified Friedman-Robertson-Walkers (FRW) equation in the form of first law of thermodynamics at the apparent horizon. We consider the universe filled with the viscous fluid. Here we employ the general expression of temperature gravity and entropy at the apparent horizon of FRW universe and obtain the generalized first law of thermodynamics at the special condition for the modified FRW equation. The generalized first law of thermodynamics help us to arrange the α ₁, α ₂, β ₁ and β ₂ in modified Friedman-Robertson-Walkers equation.     

Dynamics of charged bulk viscous collapsing cylindrical source with heat flux

In this paper, we have explored the effects of dissipation on the dynamics of charged bulk viscous collapsing cylindrical source which allows the out-flow of heat flux in the form of radiations. The Misner–Sharp formalism has been implemented to drive the dynamical equation in terms of proper time and radial derivatives. We have investigated the effects of charge and bulk viscosity on the dynamics of collapsing cylinder. To determine the effects of radial heat flux, we have formulated the heat transport equations in the context of Müller–Israel–Stewart theory by assuming that thermodynamics viscous/heat coupling coefficients can be neglected within some approximations. In our discussion, we have introduced the viscosity by the standard (non-causal) thermodynamics approach. The dynamical equations have been coupled with the heat transport equation; the consequences of the resulting coupled heat equation have been analyzed in detail.     

Causal Heat Transport in Inhomogeneous Cosmologies

We investigate the effect of heat dissipation in inhomogeneous cosmologies by invoking the full causal theory of heat transport within the framework of extended irreversible thermodynamics. This work extends earlier results which were obtained using the truncated causal heat transport equation. In particular, we show that the truncation of the heat transport equation implicitly defines a temperature law which leads to pathological behaviour in the temperature of the evolving cosmic fluid.     

On relativistic thermodynamics

The thermodynamics of moving bodies is developed from first principles. To do this, it is necessary to augment the laws of thermodynamics with a new principle, which asserts the impossibility of thermal equilibrium between bodies in relative motion. Clausius' theorem is generalized to heat flow between moving systems, and leads naturally to the identification of heat and temperature as Lorentz scalars. The formulation of relativistic statistical mechanics is carried out and the correspondence with classical quantities is made. The quantum distribution laws are generalized to the relativistic case, and are found to differ from their accepted relativistic form.     

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.     

Mass transport theory for the Toda lattices, dispersive and dissipative

To establish mass transport theory on nonlinear lattices, we formulate the Korteweg–deVries (KdV) equation and the Burgers equation using the flow variable representation so as to facilitate comparison with the Boltzmann equation and with the Cahn–Hilliard equation in classical statistical mechanics. We also study Toda lattice microdynamics using the Flaschka representation, and compare with the Liouville equation. Like the linear diffusion equation, the Boltzmann equation and the Liouville equation are to be solved for a distribution function, which is intrinsically probabilistic. Transport theory in linear systems is governed by the isotropic motions of the kinetic equations. In contrast, the KdV perturbation equation derived from the Toda lattice microdynamics expresses hydrodynamic mass transport. The KdV equation in hydrodynamics and the Burgers equation in thermodynamics do not involve a probability distribution function. The nonlinear lattices do not retain isotropy of the mass transport equations. In consequence, it is proposed that in the presence of hydrodynamic flows to the left, KdV wave propagation proceeds to the right. This basic property of the KdV system is extended to thermodynamics in the Burgers system. These features arise because linear systems are driven towards an equilibrium by molecular collisions, whereas the inhomogeneities of the nonlinear lattices are generated by the potential energy of interaction. Diffusion as expressed by the Burgers equation is governed not only by a chemical potential, but also by the Toda lattice potential energy.     

A new rotating black hole in quintessential dark energy and its thermodynamics

The spacetime metric for a rotating black hole in a quintessential field can take various forms owing to the ambiguity of the state equation for quintessential dark energy in rotating spacetime. Herein, to provide a more physical solution, the metric is determined by imposing the laws of thermodynamics of a black hole, which is typically valid in most systems. The new metric ensures the validity of the first and second laws of thermodynamics and can degenerate to the known non-rotating metric in the quintessential field. Moreover, we set an upper limit for the black hole rotation parameter, a, in our metric according to the weak energy condition(WEC).     

Exact results on random bond Ising Chains in magnetic fields

In this contribution we present exact results on the random bond Ising Chain in a magnetic field. The original problem is reduced to the solution of a functional equation for a certain probability distribution, which can be used to evaluate thermodynamics and correlation functions. We give a sufficiently accurate solution for low temperatures, which yields the complete low-temperature behaviour. Comparison is made with different Monte-Carlo-calculations performed on this system.Work supported in part by the Deutsche Forschungs-gemeinschaft     

Thermodynamics and weak cosmic censorship conjecture of charged AdS black hole in the Rastall gravity with pressure

Treating the cosmological constant as a dynamical variable, we investigate the thermodynamics and weak cosmic censorship conjecture(WCCC) of a charged Ad S black hole(BH) in the Rastall gravity. We determine the energy momentum relation of charged fermion at the horizon of the BH using the Dirac equation. Based on this relation, it is shown that the first law of thermodynamics still holds as a fermion is absorbed by the BH. However, the entropy of both the extremal and near-extremal BH decreases in the irreversible process, which means that the second law of thermodynamics is violated.Furthermore, we verify the validity of the WCCC by the minimum values of the metric function h(r) at its final state. For the extremal charged Ad S BH in the Rastall gravity, we find that the WCCC is always valid since the BH is extreme. While for the case of near-extremal BH, we find that the WCCC could be violable in the extended phase space(EPS), depending on the value of the parameters of the BH and their variations.     

Quantum corrections to the entropy in a driven quantum Brownian motion model

The quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics.In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. We obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy in the weak coupling limit. Moreover, we find that for the thermodynamic equilibrium initial state, all terms odd in h are exactly zero. Our results bring important insights to the understanding of entropy in open quantum systems.     

Stability of droplets and channels on homogeneous and structured surfaces

Wetting of structured or imprinted surfaces which leads to a variety of different morphologies such as droplets, channels or thin films is studied theoretically using the general framework of surface or interface thermodynamics. The first variation of the interfacial free energy leads to the well-known Laplace equation and a generalized Young equation which involves spatially dependent interfacial tensions. Furthermore, we perform the second variation of the free energy for arbitrary surface patterns and arbitrary shape of the wetting morphology in order to derive a new and general stability criterion. The latter criterion is then applied to cylindrical segments or channels on homogeneous and structured surfaces. Received 4 August 1999     

Response to Z. Banach's comments on the modified moment method and irreversible thermodynamics

In this paper the author responds to the comments on the modified moment method and irreversible thermodynamics made by Z. Banach [Physica A 145 (1987) 105]. In this paper Banach suggests a variational method in which the Lagrange multipliers are determined from the constraints alone by disregarding the entropy balance equation. It is shown that since this method does not yield an extended Gibbs relation consistent with the entropy balance equation or the H-theorem, there is no irreversible thermodynamics formalism afforded by the method. Consequently, his criticism cannot be supported from the viewpoint of irreversible thermodynamics. It is also pointed out that neither is there a mathematical and physical support for the criticism he makes on the cumulant expansion for the Boltzmann collision integral.