In recent years, the thermodynamic properties of black holes are topics of interests. We investigate the thermodynamic properties like surface gravity and Hawking temperature on event horizon of regular black holes viz. {\it Hayward Class} and {\it asymptotically AdS (Anti-de Sitter)} black holes. We also analyze the {\it thermodynamic volume} and {\it naive geometric volume} of asymptotically AdS black holes and show that the entropy of these black holes is simply the ratio of the naive geometric volume to thermodynamic volume. We plot the different graphs and interpret them physically. We derive the {\it `cosmic-Censorship-Inequality'} for both type of black holes. Moreover, we calculate {\it the thermal heat capacity} of aforesaid black holes and study their stability in different regimes. Finally, we compute the logarithmic correction to the entropy for both the black holes considering the quantum fluctuations around the thermal equilibrium and study the corresponding thermodynamics.
We study the irreversible (non-equilibrium) thermodynamics of FRW universe containing only dark energy. Using the modified entropy-area relation which is motivated from the loop quantum gravity, we calculate the entropy-corrected form of the apparent horizon of FRW universe.
Based on a recent proposal for the volume inside a black hole, we calculate the entropy associated with this volume and show that such entropy is proportional to the surface area of the black hole. Together with the consideration of black hole radiation, we find that the thermodynamics associated with the entropy is likely to be caused by the vacuum polarization near the horizon.
Universal thermodynamics for FRW model of the Universe bounded by apparent/event horizon has been considered for massive gravity theory. Assuming Hawking temperature and using the unified first law of thermodynamics on the horizon, modified entropy on the horizon has been determined. For simple perfect fluid with constant equation of state, generalized second law of thermodynamics and thermodynamical equilibrium have been examined on both the horizons.
Entanglement entropy is often speculated as a strong candidate for the origin of the black-hole entropy. To judge whether this speculation is true or not, it is effective to investigate the whole structure of thermodynamics obtained from the entanglement entropy, rather than just to examine the apparent structure of the entropy alone or to compare it with that of the black hole entropy. It is because entropy acquires a physical significance only when it is related to the energy and the temperature of a system. From this point of view, we construct a `thermodynamics of entanglement' by introduc…
The comment arXiv:1204.2729v1 is completely wrong. The author makes serious mistakes in calculations and judgement. The errors are made at the level of basic undergraduate statistical mechanics.
On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In the first part of the paper, a general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced which makes it possible, firstly, to judge special assumptions for the entropy density 4-vector made by other authors with respect to their generality and validity and, secondly, to determine entropy supply and e…
The paper deals with universal thermodynamics for FRW model of the universe bounded by apparent (or event) horizon. Assuming Hawking temperature on the horizon, the unified first law is examined on the horizon for different gravity theories. The results show that equilibrium configuration is preserved with a modification to Bekenstein entropy on the horizon.
We discuss the thermodynamic limit in the canonical area ensemble used in loop quantum gravity to model quantum black holes. The computation of the thermodynamic limit is the rigorous way to obtain a smooth entropy from the counting entropy given by a direct determination of the number of microstates compatible with macroscopic quantities (the energy in standard statistical mechanics or the area in the framework presented here). As we will show in specific examples the leading behavior of the smoothed entropy for large horizon areas is the same as the counting entropy but the subleading contri…
We investigate the thermodynamic arrow of time in a time-symmetrically recollapsing universe by calculating quantum mechanically the entropy production of a massive scalar field. It is found that even though the Hamiltonian has a time-reversal symmetry with respect to the maximum expansion of the universe, the entropy production is generic and the total entropy of the scalar field increases monotonically. We conclude that the thermodynamic arrow of time is a universal phenomenon even in the expanding and subsequently recollapsing universe due to the parametric interaction of matter field with …
This work is to study the generalized second law (GSL) of thermodynamics in tachyon cosmology where the boundary of the universe is assumed to be enclosed by a dynamical apparent horizon. The model is constrained with the observational data. The two logarithmic and power law corrected entropy is also discussed and conditions to validate the GSL and corrected entropies are obtained.
Entanglement entropy is a statistical entropy measuring information loss due to coarse-graining corresponding to a spatial division of a system. In this paper we construct a thermodynamics (entanglement thermodynamics) which includes the entanglement entropy as the entropy variable, for a massless scalar field in Minkowski, Schwarzschild and Reissner-Nordstr{ö}m spacetimes to understand the statistical origin of black-hole thermodynamics. It is shown that the entanglement thermodynamics in Minkowski spacetime differs significantly from black-hole thermodynamics. On the contrary, the entangleme…
In black hole physics, the second law of thermodynamics is generally valid whether the black hole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of black hole dynamics extends to the non-negativity of the sum of the entropy of the matter and the horizon, known as generalized second law of thermodynamics(GSLT). Here, we have assumed the universe to be bounded by the event-horizon where Bekenstein entropy-area relation and Hawking-temperature are not applicable. Thus considering entropy to be an arbitrary function of the area of the event-hor…
In this work we have investigated the effects of three nongaussian entropies, namely, the modified Rényi entropy (MRE), the Sharma-Mittal entropy (SME) and the dual Kaniadakis entropy (DKE) in the investigation of the generalized second law (GSL) of thermodynamics violation. The GSL is an extension of the second law for black holes. Recently, it was concluded that a total entropy is the sum of the entropy enclosed by the apparent horizon plus the entropy of the horizon itself when the apparent horizon is described by the Barrow entropy. It was assumed that the universe is filled with matter an…
For analyzing the thermodynamical behavior of two well-known black holes such as RN-AdS black hole with global monopole and $f(R)$ black hole, we consider the higher order logarithmic corrected entropy. We develop various thermodynamical properties such as, entropy, specific heats, pressure, Gibb's and Helmhotz free energies for both black holes in the presence of corrected entropy. The versatile study on the stability of black holes is being made by using various frameworks such as the ratio of heat capacities ($γ$), grand canonical and canonical ensembles, and phase transition in view of hig…
Non-equilibrium and equilibrium thermodynamics of an interacting component in a special-relativistic multi-component system is discussed by use of an entropy identity. The special case of the corresponding free component is considered. Equilibrium conditions and especially the multi-component Killing relation of the 4-temperature are discussed. Two axioms characterize the mixture: additivity of the energy momentum tensors and of the 4-entropies of the components generating those of the mixture. The resulting quantities of a component and of the mixture, energy, energy flux, momentum flux, stre…
The entropy of a black hole can differ from a quarter of the area of the horizon because of quantum corrections. The correction is related to the contribution to the Euclidean functional integral from quantum fluctuations but is not simply equal to the correction to the effective action. A (2+1) dimensional rotating black hole is explicitly considered.
In this work we have investigated the effects of the two highlighted nongaussian entropies which are the modified Rényi entropy and the so-called Incomplete statistics in the analysis of the thermodynamics of black holes (BHs). We have obtained the equipartition theorems and after that we obtained the heat capacities for both approaches. Depending on the values of both $λ-$parameter and $M$, the BH mass, relative to a modified Rényi entropy and, depending on the values of the $q-$parameter and $M$, the Incomplete entropy can determine if the BH has an unstable thermal equilibrium or not for ea…
There is a deep underlying problem in the model dependent thermodynamic analysis of black holes shown in the above quoted paper. In this method one can only find out the canonical entropy of the black hole but not the `microcanonical' entropy. Besides this crucial issue a few other problems are also discussed.
While the Bekenstein-Hawking entropy is the unique notion of entropy that makes classical black hole thermodynamics consistent, alternative entropy notions (Rényi, Tsallis, and generalized constructs) abound in the literature. We explore conditions under which they are part of a consistent horizon thermodynamics for certain classes of modified gravity black holes. We provide examples in which black hole masses and temperatures going hand-in-hand with these alternative entropies coincide with their usual counterparts associated with the Bekenstein-Hawking entropy.
The comparison of geometrical properties of black holes with classical thermodynamic variables reveals surprising parallels between the laws of black hole mechanics and the laws of thermodynamics. Since Hawking's discovery that black holes when coupled to quantum matter fields emit radiation at a temperature proportional to their surface gravity, the idea that black holes are genuine thermodynamic objects with a well-defined thermodynamic entropy has become more and more popular. Surprisingly, arguments that justify this assumption are both sparse and rarely convincing. Most of them rely on an…
We study spacetime thermodynamics for non-equilibrium processes. We first generalize the formulation of spacetime thermodynamics by using an observer outside the horizon. Then we construct the entropy balance equation of spacetime thermodynamics for non-equilibrium processes in f(R) gravity. The coefficients of the expansion and shear terms are equal to the viscosities of the black hole membrane paradigm, and a new entropy production term appears.
We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical entropy calculated according to 't Hooft and regularized by Pauli-Villars.
We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both black branes and black holes to Wald's Noether charge entropy. We support the thermodynamic interpretation of the proposed entropy by showing that, for some cases, the field theory duals of the entropy, energy and pressure are the same as the corresponding quantities in the field theory. In this context, the Einstein equations are equivalent to the field the…
The thermodynamical one-loop entropy $S^{TD}$ of a two-dimensional black hole in thermal equilibrium with the massless quantum gas is calculated. It is shown that $S^{TD}$ includes the Bekenstein-Hawking entropy, evaluated for the quantum corrected geometry, and the finite difference of statistical mechanical entropies $-Tr\hatρ\ln\hatρ$ for the gas on the black hole and Rindler spaces. This result demonstrates in an explicit form that the relation between thermodynamical and statistical-mechanical entropies of a black hole is non-trivial and requires special subtraction procedure.
The extended black hole thermodynamics in which the cosmological constant plays the role of pressure significantly enriches the phase structure of the theory. In order to understand the extended black hole thermodynamics more precisely, we let the value of the cosmological constant vary dynamically via tunneling from one vacuum to another in a black hole induced vacuum decay. In this process, entropy of the matter/energy released by a black hole is crucial to validate the second law of thermodynamics. In other words, without taking this bulk entropy into account, entropy associated with the bl…
In black hole thermodynamics of certain models, the thermodynamic first law may contain the pressure term. The corresponding entropy follows the area law whereas the thermodynamic energy is not the same with the black hole mass. If the pressure can be decomposed into two parts and recombined with the original thermodynamic quantities, then the thermodynamic energy becomes the black hole mass and the entropy satisfying the area law turns out to be the corrected entropy called the Wald entropy, respectively.
We review some recent advances in black hole thermodynamics, including statistical mechanical origins of black hole entropy and its leading order corrections, from the viewpoints of various quantum gravity theories. We then examine the information loss problem and some possible approaches to its resolution. Finally, we study some proposed experiments which may be able to provide experimental signatures of black holes.
We discuss the first law of thermodynamics of Bardeen black hole. The presence of magnetic monopole charge modifies the energy and we define the temperature of the system accordingly. We introduce a lower cut-off to the space time by introducing a spherical surface, which can be identified with the event horizon. The corresponding temperature is identified with Hawking temperature. The entropy is assumed to obey the area law and we confirm this by calculating the statistical entropy by using brick wall model.
We present a statistical mechanical calculation of the thermodynamical properties of (non rotating) isolated horizons. The introduction of Planck scale allows for the definition of an universal horizon temperature (independent of the mass of the black hole) and a well-defined notion of energy (as measured by suitable local observers) proportional to the horizon area in Planck units. The microcanonical and canonical ensembles associated with the system are introduced. Black hole entropy and other thermodynamical quantities can be consistently computed in both ensembles and results are in agreem…
We investigate the thermodynamic behaviour of Lorentzian Dyonic Taub-NUT Black Hole spacetimes. We consider two possibilities in their description: one in which their entropy is interpreted to be one quarter of the horizon area (the horizon entropy), and another in which the Misner string also contributes to the entropy (the Noether charge entropy). We find that there can be as many as three extremal black holes (or as few as zero) depending on the choice of parameters, and that the dependence of the free energy on temperature -- and the resultant phase behaviour -- depends very much on which …
For a general maximally symmetric (spherically, plane or hyperbola symmetric) holographic screen, we rewrite the equations of motion of general Lovelock gravity into the form of some generalized first law of thermodynamics, under certain ansatz. With this observation together with other two independent ways, exactly the same temperature and entropy on the screen are obtained. So it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general maximally symmetric screen. Moreover, the formula of entropy is further checked in t…
Based on the entropy relations, we derive thermodynamic bound for entropy and area of horizons of Schwarzschild-dS black hole, including the event horizon, Cauchy horizon and negative horizon (i.e. the horizon with negative value), which are all geometrical bound and made up of the cosmological radius. Consider the first derivative of entropy relations together, we get the first law of thermodynamics for all horizons. We also obtain the Smarr relation of horizons by using the scaling discussion. For thermodynamics of all horizons, the cosmological constant is treated as a thermodynamical varia…
Recently, there has been much attention devoted to resolving the quantum corrections to the Bekenstein-Hawking (black hole) entropy, which relates the entropy to the cross-sectional area of the black hole horizon. Using generalized uncertainty principle (GUP), corrections to the geometric entropy and thermodynamics of black hole will be introduced. The impact of GUP on the entropy near the horizon of three types of black holes; Schwarzschild, Garfinkle-Horowitz-Strominger and Reissner-Nordström is determined. It is found that the logarithmic divergence in the entropy-area relation turns to be …
We derive the Einstein field equations and black hole entropy from the first law of thermodynamics on a holographic time-like screen. Because of the universality of gravity, the stress tensor on the screen must be independent of the details of matter fields, so it should be a pure geometric quantity. For simplicity, we assume that the stress tensor on the screen depends on surface Ricci curvature and extrinsic curvature linearly. Then we prove that the surface stress tensor is just the Brown-York stress tensor plus terms which do not affect the field equations of gravitation and the entropy of…
We introduce a new interpretation of chemical potential and show that holographic entropy is entropy bound, which is supported by two ideal cases discussed in detail. One is sparse but incompressible liquid like a star of uniform density and the other is a screen at infinity in spherically symmetric sapcetime. Our work is based on the new scenario of entropy force and holographic thermodynamics, and the Brown-York quasi-local energy.
We find that the ambiguity term of approximate Killing vector field is responsible for the entropy production term. Without the ambiguity term, pure Einstein theory and $f(R)$ satisfy the relation of thermodynamic equilibrium. Considering such an ambiguity term of approximate Killing vector field, we can get the entropy production term and the entropy in $f(R)$ with a form defined by Jacobson. In pure Einstein theory, the shear term is the only geometric contribution of entropy production term, while in $f(R)$ it can also contribute. We believe our approach and conclusion can be generalized to…
We investigate the validity of the generalized second law of thermodynamics, applying Barrow entropy for the horizon entropy. The former arises from the fact that the black-hole surface may be deformed due to quantum-gravitational effects, quantified by a new exponent $Δ$. We calculate the entropy time-variation in a universe filled with the matter and dark energy fluids, as well as the corresponding quantity for the apparent horizon. We show that although in the case $Δ=0$, which corresponds to usual entropy, the sum of the entropy enclosed by the apparent horizon plus the entropy of the hori…
The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional flat spacetime is analyzed. Inside the ring the spacetime is flat, whereas outside it is conical flat. The first law of thermodynamics applied to the thin shell leads to a shell's entropy which is a function of its mass alone. Two simple forms for this mass function are given leading to two different expressions for the entropy. The equations of thermodynamic stability are analyzed resulting in certain allowed regions for the free parameters. Contrary to the usual (3+1)-dimensional case this shell's entropy…
I consider the thermodynamics of the BTZ black hole in the presence of the higher curvature and gravitational Chern-Simons terms, and its statistical entropy. I propose a new thermodynamical entropy, which being {\it non-negative} manifestly, such as the second law, as well as the first law, of thermodynamics is satisfied. I show that the new \therl entropy agrees perfectly with the statistical entropy for $all$ the values of the conformal factor of the higher curvature terms and the coupling constant of the gravitational Chern-Simons term, in contrast to some disagreements in the literatures.…
We review recent progress in understanding certain aspects of the thermodynamics of black holes and other horizons. Our discussion centers on various ``entropy bounds'' which have been proposed in the literature and on the current understanding of how such bounds are {\it not} required for the semi-classical consistency of black hole thermodynamics. Instead, consistency under certain extreme circumstances is provided by two effects. The first is simply the exponential enhancement of the rate at which a macrostate with large entropy is emitted in any thermal process. The second is a new sense i…
We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal non-uniform time translation $t\to t+η\hbar β$, where $η$ is a small parameter, $\hbar$ is the Planck constant, $β$ is the inverse temperature that depends on the energy and control parameter, and trajectories in the phase space are restricted to those consistent with quasi-static processes in thermodynamics.
A power-law corrected entropy based on a quantum entanglement is considered to be a viable black-hole entropy. In this study, as an alternative to Bekenstein-Hawking entropy, a power-law corrected entropy is applied to Padmanabhan's holographic equipartition law to thermodynamically examine an extra driving term in the cosmological equations for a flat Friedmann-Robertson-Walker universe at late times. Deviations from the Bekenstein-Hawking entropy generate an extra driving term (proportional to the $α$-th power of the Hubble parameter, where $α$ is a dimensionless constant for the power-law c…
We take up the question why the initial entropy in the universe was small, in the context of evolution of the entropy of a classical system. We note that coarse-graining is a an important aspect of entropy evaluation which can reverse the direction of the increase in entropy, i.e., the direction of thermodynamic arrow of time. Then we investigate the role of decoherence in the selection of coarse-graining and explain how to compute entropy for a decohered classical system. Finally, we argue that the requirement of low initial entropy imposes constraints on the decoherence process.
We are discussing a universal non-unitary map M subsequent to a generic unitary map U, whose von Neumann entropy gain coincides with the calculated thermodynamic entropy production. For many-body quantum reservoirs we prove that M can be the averaging over all translations of the spatial frame. Assuming the coincidence of microscopic and macroscopic entropy productions leads to a novel equation between entropy gain of frame averaging and relative entropy. Our map M turns out to coincide with the older one called twirl, used recently in the theory of quantum reference frames. Related results to…
One of the most intriguing features of string thermodynamics is thermal duality, which relates the physics at temperature T to the physics at inverse temperature 1/T. Unfortunately, the traditional definitions of thermodynamic quantities such as entropy and specific heat are not invariant under thermal duality transformations. In this paper, we propose several novel approaches towards dealing with this issue. One approach yields a "bootstrap" method of extracting possible exact, closed-form solutions for finite-temperature effective potentials in string theory. Another approach involves extend…
