In this paper we have investigated the limits imposed by thermodynamics on a dark energy fluid. We have obtained the heat capacities and the compressibilities for a dark energy fluid. The thermal and mechanical stabilities require these quantities to be positive. We have shown that dark energy fluids must satisfy the stability conditions and that such requirement put difficulties in the cosmic fluid models with negative constant EoS parameters. We have also shown that the observational constraints imposed by SN Ia, BAO and $H(z)$ data on a general dark energy fluid with a time-dependent EoS parameter are in conflict with the constraints imposed by thermodynamics. This result indicates that dark energy fluid models are unphysical.
We establish the nonlocal generalization of the Israel-Stewart model for the relativistic causal thermodynamics of the cosmic fluid, which evolves in the homogeneous isotropic Universe. Based on the second law of thermodynamics we derive the integro-differential master equation for the nonequilibrium pressure scalar and reduce it to the differential equation of the second order in time derivatives. We show that this master equation can be considered as the relativistic analog of the Burgers equation, which is known in the classical theory of viscoelasticity. We obtain the nonlinear key equatio…
In this paper, we study the model of $f(T, B)$ gravity with viscous fluid in flat-FRW metric, in which $T$ and $B$ are torsion scalar and boundary term, respectively. We obtain the Friedmann equations in the framework of modified teleparallel gravity by tetrad components. We consider an interacting model between matter and dark energy so that universe dominates by viscous fluid. Then, we write the corresponding cosmological parameters in terms of the redshift parameter, and, we parameterize the Hubble parameter with experimental data. In what follows, we plot the corresponding cosmological par…
We analyze the interpretation of the spherically symmetric perfect fluid solutions that admit a flat synchronization orthogonal to the fluid flow as a thermodynamic perfect fluid in local thermal equilibrium. The ideal gas sonic condition is examined for this family of metrics, and the macroscopic conditions for physical reality are accurately tested for some specific solutions.
In spite of a recent reply by Quevedo and Zárate (gr-qc/0403096), their assertion that their thermodynamic scheme for a perfect fluid binary mixture is incompatible with Szekeres and Stephani families of universes, except those of FRW ones, remains wrong.
We study the thermodynamics of the universe containing perfect fluid with equation of state $p=ωρ,ω$ is variable. Here we choose $ω$ to be a function of the red shift variable $z$ and four different choices of $ω$ has been investigated. Also the laws of thermodynamics are examined considering the universe bounded by the horizon (apparent) as a thermodynamical system.
The low-energy dynamics of relativistic continuous media is given by a shift-symmetric effective theory of four scalar fields. These scalars describe the embedding in spacetime of the medium and play the role of Stückelberg fields for spontaneously broken spatial and time translations. Perfect fluids are selected imposing a stronger symmetry group or reducing the field content to a single scalar. We explore the relation between the field theory description of perfect fluids to thermodynamics. By drawing the correspondence between the allowed operators at leading order in derivatives and the th…
The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In relativistic fluid mechanics, positive entropy production is known to be insufficient for guaranteeing stability. Much more restrictive criteria for thermodynamic admissibility have become available in nonequilibrium thermodynamics. We here perform a linear stability analysis for a model of relativistic hydrodynamics that is based on the GENERIC (general equation for t…
We show that the Einstein field equations with a negative cosmological constant can admit black hole solutions whose thermodynamics coincides with that of logotropic fluids, recently investigated to heal some cosmological and astrophysical issues. For this purpose, we adopt the Anton-Schmidt equation of state, which represents a generalized version of logotropic fluids. We thus propose a general treatment to obtain an asymptotic anti-de Sitter metric, reproducing the thermodynamic properties of both Anton-Schmidt and logotropic fluids. Hence, we explore how to construct suitable spacetime func…
Our aim is to investigate the thermodynamic properties of the universe bounded by the cosmological event horizon and dominated by the tachyon fluid. We give two different laws of evolution of our universe. Further, we show the first law and the generalized second law of thermodynamics (GSLT) are both satisfied in two cases, but their properties of the thermodynamic equilibrium are totally different. Besides, under our solutions, we find the validity of the laws of thermodynamics is irrelevant with the parameters of the tachyon fluid. Finally, we conclude that the universe bounded by the cosmol…
We show that the analysis presented in a recent comment by Coll and Ferrando \cite{comment} (qr-qc/0312058) is based on the erroneous assumption that the chemical potential and fractional concentration of a {\it mixture} of perfect fluids are unknown variables.
We analyze the compatibility between the geometrodynamics and thermodynamics of a binary mixture of perfect fluids which describe inhomogeneous cosmological models. We generalize the thermodynamic scheme of general relativity to include the chemical potential of the fluid mixture with non-vanishing entropy production. This formalism is then applied to the case of Szekeres and Stephani families of cosmological models. The compatibility conditions turn out to impose symmetry conditions on the cosmological models in such a way that only the limiting case of the Friedmann-Robertson-Walker model re…
This paper is devoted to investigate the thermodynamic stability of a generic cosmological fluid known as Van der Waals fluid in the context of flat FRW universe. It is treated as a perfect fluid that obeys the equation of state $P=\frac{γρ}{1-βρ}-αρ^{2}, 0\leqγ<1$, where $ρ$ stands for energy density and $P$ stands for pressure of the fluid. In this regard, we discuss the behavior of physical parameters to analyze the evolution of the universe. We investigate whether the cosmological scenario fulfills the third law of thermodynamics using specific heat formalism. Next we discuss the thermal e…
The present work deals with homogeneous and isotropic FLRW model of the Universe having a system of non-interacting diffusive cosmic fluids with barotropic equation of state (constant or variable equation of state parameter). Due to diffusive nature of the cosmic fluids, the divergence of the energy momentum tensor is chosen to be proportional to the diffusive current. The thermodynamic stability analysis of individual fluids is done and the stability conditions are expressed as restrictions on the equation of state parameter.
It is shown that inhomogeneous Szekeres and Stephani universes exist corresponding to non-dissipative binary mixtures of perfect fluids in local thermal equilibrium. This result contradicts a recent statement by Zárate and Quevedo (2004 Class. Quantum Grav. {\bf 21} 197, {\it Preprint} gr-qc/0310087), which affirms that the only Szekeres and Stephani universes compatible with these fluids are the homogeneous Friedmann-Robertson-Walker models. Thus, contrarily to their conclusion, their thermodynamic scheme do not gives new indications of incompatibility between thermodynamics and relativity. T…
A general thermodynamic treatment of dissipative relativistic fluids is introduced, where the temperature four vector is not parallel to the velocity field of the fluid. Generic stability and kinetic equilibrium points out a particular thermodynamics, where the temperature vector is parallel to the enthalpy flow vector and the choice of the flow fixes the constitutive functions for viscous stress and heat. The linear stability of the homogeneous equilibrium is proved in a mixed particle-energy flow-frame.
Thermodynamics unavoidably contains fluctuation theory, expressible in terms of a unique thermodynamic information metric. This metric produces an invariant thermodynamic Riemannian curvature scalar $R$ which, in fluid and spin systems, measures interatomic interactions. Specifically, $|R|$ measures the size of organized fluctuating microscopic structures, and the sign of $R$ indicates whether the interactions are effectively attractive or repulsive. $R$ has also been calculated for black hole thermodynamics for which there is no consensus about any underlying microscopic structures. It is hop…
In the so-called unified dark fluid models, the dark sector gets simplified because dark matter and dark energy are replaced by a single fluid that behaves as the former at early times and as the latter at late times. In this short paper we analyze this class of models from the thermodynamic viewpoint. While the second law of thermodynamics is satisfied, the first two derivatives of the entropies of the apparent horizon and of the energy components suffer such a sharp oscillation that doubts are raised about the soundness of this class of models.
We show that there is a correspondence between cosmology from non-extensive thermodynamics and cosmology with fluids of redefined and generalized equation of state. We first establish the correspondence in the case of basic non-extensive thermodynamics, and then we proceed by investigating the more consistent case, from the quantum field theoretical point of view, of varying exponent, namely depending on the scale. The obtained duality provides a way of explaining the complicated phenomenological forms of the effective fluid equation-of-state parameters that are being broadly used in the liter…
This article presents the study of a multi-species fluid characterised by a freeze-out or break-away of one or more species. Whereas single-fluid approximation suffices for modelling of the pre {\it freeze-out} period, multi-fluid approximation is required for the post freeze-out period. Embedded in this is a transition period where neither one of the two approximations is singly appropriate. We examine the thermodynamics of this fluid and find that the second law holds before, during and after the freeze-out. Our application to cosmological modelling involving interacting dark-section species…
We provide a proof of the necessary and sufficient condition on the profile of the temperature, chemical potential, and angular velocity for a charged perfect fluid in dynamic equilibrium to be in thermodynamic equilibrium not only in fixed but also in dynamical electromagnetic and gravitational fields. In passing, we also present the corresponding expression for the first law of thermodynamics for such a charged star.
Thermodynamics on the cosmological apparent horizon of a flat Friedmann-Lemaitre-Robertson-Walker metric has been investigated with Bekenstein entropy and Hawking temperature on the horizon, and Unruh temperature for the fluid inside the horizon. This temperature is experienced by a radial comoving observer infinitesimally close to the horizon due to the pressure exerted by the fluid bounded by the horizon. An expression for the entropy of the fluid has been obtained which is found to be proportional to the volume of the thermodynamic system which implies that the Unruh temperature of the flui…
We investigate the emergent universe scenario in the presence of interacting fluids. The non-linear equation of state (EoS) considered in the general theory of relativity for obtaining emergent universe is effectively a cosmological model with a composition of three fluids. In this paper we consider two models to realize viable cosmological scenarios, {\it viz.}, (i) a two-fluid model with interaction of a pressureless fluid with the fluid having the non-linear EoS needed for the emergent universe, and (ii) a three-fluid model with interaction among the three fluids which originate from the Eo…
We demonstrate that the thermodynamics of a perfect fluid describing baryonic matter can, in certain limits, lead to an equation of state similar to that of dark energy. We keep the cosmic fluid equation of state quite general by just demanding that the speed of sound is positive and less than the speed of light. In this framework, we discuss some propositions by looking at the asymptotic behavior of the cosmic fluid.
Based on Reissner-Nordstrom-anti-de Sitter(RN-AdS) black hole surrounded by perfect fluid dark matter, we study the thermodynamics and phase transition by extending the phase space defined by the charge square $Q^{2}$ and the conjugate quantity $ψ$, where $ψ$ is a function of horizon radius. The first law of thermodynamics and the equation of state are derived in the form $Q^{2}=Q^{2}(T,ψ)$. By investigating the critical behaviour of perfect fluid dark matter around Reissner-Nordstrom-anti-de Sitter black hole, we find that these thermodynamics system are similar to Van der Waals system, and c…
This article extends the single-fluid relativistic irreversible thermodynamics theory of {\it M{ü}ller}, {\it Israel} and {\it Stewart} (hereafter the {MIS} theory) to a multi-fluid system with inherent species interactions. This is illustrated in a two-fluid toy-model where an effective complex 4-velocity plays the role of a primary dynamical parameter. We find that an observer who resides in the {\it real}-part of this universe will notice that their knowledge of the universe parametrized using {\it real}, rather than {\it imaginary}, quantities are insufficient to fully determine properties…
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.
According to maximum entropy principle, it has been proved that the gravitational field equations could be derived by the extrema of total entropy for perfect fluid, which implies that thermodynamic relations contain information of gravity. In this manuscript, we obtain a criterion for thermodynamical stability of an adiabatic, self-gravitating perfect fluid system by the second variation of total entropy. We show, for Einstein's gravity with spherical symmetry spacetime, that the criterion is consistent with that for dynamical stability derived by Chandrasekhar and Wald. We also find that the…
The thermodynamic behaviour of a relativistic perfect simple fluid obeying the equation of state $p=(γ-1)ρ$, where $0 \le γ\le 2$ is a constant, has been investigated. Particular cases include: vacuum($p=-ρ$, $γ=0$), a randomly oriented distribution of cosmic strings ($p=-{1 \over 3} ρ$, $γ=2/3$), blackbody radiation ($p={1\over 3} ρ$, $γ=4/3$) and stiff matter ($p=ρ$, $γ=2$). Fluids with $γ<1$ become hotter when they expand adiabatically ($T\propto V^{1- γ}$). By assuming that such fluids may be regarded as a kind of generalized radiation, the general Planck's type form of the spectrum is ded…
The work deals with the thermodynamical aspects of the cosmic substratum which is dissipative in nature. For homogeneous and isotropic model of the Universe this dissipative phenomenon is effective bulk viscous pressure in nature and is related to the particle creation mechanism. Finally, the stability criteria for the thermal equilibrium has been analyzed and are presented in tabular form restricting the particle creation parameter or the variation of the equation of state parameter with the volume.
The present work deals with three alternative generalized Bekenstein-Hawking formulation of thermodynamical parameters namely entropy and temperature for the universal thermodynamical system bounded by a horizon in the frame work of inhomogeneous perfect fluid Lemaitre-Tolman-Bondi (LTB) model of the Universe. For the first choice, the first law of thermodynamics holds only for the trivial de Sitter case of the LTB model while we need restriction on the evolution of the horizon radius for the validity of the generalized second law of thermodynamics. However, for the other two choices, the firs…
We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve {\em 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 {\em 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 (s…
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
We reveal unifying thermodynamic aspects of so different phenomena as the cosmological electron-positron annihilation, the evaporation of primordial black holes with a narrow mass range, and the ``deflationary'' transition from an initial de Sitter phase to a subsequent standard Friedmann-Lema\^ıtre-Robertson-Walker begin (FLRW) behavior.
We present a relativistic model describing a thin disk system composed of two fluids. The system is surrounded by a halo in the presence of a non-trivial electromagnetic field. We show that the model is compatible with the variational multi-fluid thermodynamics formalism, allowing us to determine all the thermodynamic variables associated with the matter content of the disk. The asymptotic behaviour of these quantities indicates that the single fluid interpretation should be abandoned in favour of a two-fluid model.
In [1], the thermal equilibrium of static, spherically symmetric perfect fluids in General Relativity was studied. I would like to elaborate three points relevant to the results of [1]. The first point is only a clarification, summarized in theorem 1 below, of results that appear in [1]. The following two points correct the error in [1], stating that the condition for thermodynamic stability, found in [1], is referring to the microcanonical ensemble, while it was referring to the canonical one. In theorems 2 and 3, specific cases for which equivalence of dynamical and thermodynamic stability h…
The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the Generalized Second Law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we demonstrate that the accretion process is possible, and that the condition guaranteeing the positiveness of the phantom fluid entropy coincides with the one required by Generalized Second Law. In particular, this result provides a complementary confirmation that cosmological phantom fluids do not need to have negative temperatures.
We discuss the existence, stability and classical thermodynamics of four-dimensional, spherically symmetric black hole solutions of the Einstein equations with a conformally coupled scalar field. We review the solutions existing in the literature with zero, positive and negative cosmological constant. We also outline new results on the thermodynamics of these black holes when the cosmological constant is non-zero.
We determine the energy-momentum tensor of non-perfect fluids in thermodynamic equilibrium. To this end, we derive the constitutive equations for energy density, isotropic and anisotropic pressure as well as for heat-flux from the corresponding propagation equations and by drawing on Einstein's equations. Following Obukhov at this, we assume the corresponding space-times to be conform-stationary and homogeneous. This procedure provides these quantities in closed form, i.e., in terms of the structure constants of the three-dimensional isometry group of homogeneity and, respectively, in terms of…
Out of several possible extensions of general relativity, the scalar-tensor theory is the most popular for several reasons. Since the quantum description of gravity is yet to be formulated properly, the understanding of a gravitational theory remains incomplete until the study of thermodynamic and fluid-gravity aspects, which provides an alternative viewpoint to understand the gravitational theory. In this review, we study these features (thermodynamics and the fluid gravity analogy) in a rigorous and yet in a concise manner for the scalar-tensor gravity, which has been revealed in our recent …
We describe the evolution of the early and late universe from thermodynamic considerations, using the generalized non-extensive Tsallis entropy with a variable exponent. A new element in our analysis is the inclusion of a bulk viscosity in the description of the cosmic fluid. Using the generalized Friedmann equation, a description of the early and the late universe is obtained.
This paper presents a hydrodynamic and thermodynamic treatment of a radiant star model that undergoes a dissipative gravitational collapse, from a certain initial configuration until it becomes a black hole. The collapsing star consists of a locally anisotropic non-perfect fluid, where we explore the consequences of including viscous pressures, both shear and bulk viscosities, as well as radial heat flow. We analyze the temporal evolution of the heat flux, mass function, luminosity perceived by an observer at infinity and the effective surface temperature. It is shown that this simple exact mo…
In what follows, we investigate the relation between the Friedmann and thermodynamic pressure equations, through solving the Friedmann and thermodynamic pressure equations simultaneously. Our investigation shows that a perfect fluid, as a suitable solution for the Friedmann equations leading to the standard modelling of the universe expansion history, cannot simultaneously satisfy the thermodynamic pressure equation and those of Friedmann. Moreover, we consider various energy definitions, such as the Komar mass, and solve the Friedmann and thermodynamic pressure equations simultaneously to get…
We present a new approach to the problem of the thermodynamical equilibrium of a quantum relativistic fluid in a curved spacetime in the limit of small curvature. We calculate the mean value of local operators by expanding the four-temperature Killing vector field in Riemann normal coordinates about the same spacetime point and we derive corrections with respect to the flat spacetime expressions. Thereby, we clarify the origin of the terms proportional to Riemann and Ricci tensors introduced in general hydrodynamic expansion of the stress-energy tensor.
Thermodynamic acceptability of spherically symmetric perfect-fluid solutions in general relativity
Al-Farabi Kazakh National University（阿拉伯·法拉比哈萨克国立大学）；Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and ICRA, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）
We present a simple and self-consistent cosmology with a phenomenological model of quantum creation of radiation and matter due to decay of the cosmological constant $Λ$. The decay drives a non-isentropic inflationary epoch, which exits smoothly to the radiation-dominated era, without reheating, and then evolves to the dust era. The initial vacuum for radiation and matter is a regular Minkowski vacuum. The created radiation and matter obeys standard thermodynamic laws, and the total entropy produced is consistent with the accepted value. This paper is an extension of the model with the decayin…
Isotropic and spatially homogeneous viscous fluid cosmological models are investigated using the truncated Israel-Stewart theory of irreversible thermodynamics to model the bulk viscous pressure. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is then utilized to complete the system. The resulting dynamical system is analyzed using geometric techniques from dynamical systems theory to find the qualitative behaviour of the Friedmann-Robertson-Walker models with bulk viscosity. In these models there exist…
The approach of extended irreversible thermodynamics consists of promoting the dissipative fluxes to non-equilibrium thermodynamic variables. In a relativistic context, this naturally leads to the formulation of the theory of Israel and Stewart (1979), which is, to date, one of the most successful theories for relativistic dissipation. Although the generality of the principle makes it applicable to any dissipative fluid, a connection of the Israel-Stewart theory with microphysics has been established, through kinetic theory, only for the case of ideal quantum gases. By performing a convenient …
A new entropic gravity inspired derivation of general relativity from thermodynamics is presented. This generalizes, within Einstein gravity, the "Thermodynamics of Spacetime" approach by T. Jacobson, which relies on the Raychaudhuri evolution equation. Here the rest of the first law of thermodynamics is incorporated by using the Damour-Navier-Stokes equation, known from the membrane paradigm for describing fluid dynamics on the horizon.
In this paper, we study thermodynamics and thermodynamic geometry of a black hole surrounded by the perfect fluid in Rastall theory. In particular, we calculate the physical quantity like mass, temperature and heat capacity of the system for two different cases. From the resulting heat capacity, we emphasize stability of the system. Following Weinhold, Ruppiner, Quevedo and HPEM formalism, thermodynamic geometry of this black hole in Rastall gravity is also analyzed. We find that the singular points of the curvature scalar of Ruppeiner and HPEM metrics entirely coincides with zero points of th…
We review and correct the classical critical exponents characterizing the transition from negative to positive black hole's heat capacity at high charge--angular momentum. We discuss the stability properties of black holes as a thermodynamic system in equilibrium with a radiation bath (canonical ensamble) by using the Helmholtz free energy potential. We finally analytically extend the analysis to negative mass holes and study its thermodynamical stability behavior.
Thermodynamic compatibility, holographic property and wave-function representation of generalized weakly nonlocal self-gravitating non-relativistic fluids
Budapest University of Technology and Economics（布达佩斯科技经济大学）；HUN-REN Wigner Research Centre for Physics（匈牙利研究与教育网络维格纳物理研究中心）；Society for the Unity of Science and Technology（科学与技术统一协会）
