The emergence of cosmic space as cosmic time progresses is an exciting idea advanced by Padmanabhan to explain the accelerated expansion of the universe. The generalization of Padmanabhan's conjecture to the non-flat universe has resulted in scepticism about the choice of volume such that the law of emergence can not be appropriately formulated if one uses proper invariant volume. The deep connection between the first law of thermodynamics and the law of emergence \cite{mahith}, motivate us to explore the status of the first law in a non-flat universe when one uses proper invariant volume. We have shown that the first law of thermodynamics, $dE = TdS +WdV$ cannot be formulated properly for a non-flat universe using proper invariant volume. We have also investigated the status of the first law of the form $-dE = TdS$ in a non-flat universe. We have shown that the energy change dE within the horizon and the outward energy flux are not equivalent to each other in a non-flat universe when we use the proper invariant volume. We have further shown that the consistency between the above two forms of the first law claimed in Ref. \cite{caiakb} will hold only with the use of the areal volume of the horizon. Thus, a consistent formulation of the above two forms of the first law of thermodynamics demands the use of areal volume.
In this paper, we obtain the law of emergence with Tsallis entropy from the thermodynamic laws. We first derive the law of emergence from the equilibrium description of the unified first law and Clausius relation. However, it has been shown that considering Tsallis entropy as the horizon entropy, the Clausius relation $δQ=T dS$ does not hold due to non-equilibrium thermodynamics and is replaced by the entropy-balance relation $dS=\frac{δQ}{T}+d_{i}S$, where $d_iS$ is the additional entropy produced due to the irreversible thermodynamic process. Hence, we derive the law of emergence from the no…
The recent research on the connection between gravity and thermodynamics suggests that gravity could be an emergent phenomenon. Following this, Padmanabhan proposed a novel idea that the expansion of the universe can be interpreted as equivalent to the emergence of space with the progress of cosmic time. In this approach, the expansion of the universe is described by what is known as the law of emergence, which states that the expansion of the universe is driven by the difference between the number of bulk and surface degrees of freedom in a region bounded by the Hubble radius. This principle …
Recently, Barrow accounts for the quantum gravitational effects to the black hole surface. Thus the conventional area-entropy relation has modified, $S=(A/A_{0})^{1+Δ/2},$ with an exponent $Δ$, ranges $0\leΔ\le1$, quantifies the amount of quantum gravitational deformation effect to the black hole surface. In recent literature, this horizon entropy has been extended to the cosmological context. Following this, we consider an n+1 dimensional non-flat universe with an apparent horizon as the boundary with appropriate temperature and associated entropy is Barrow entropy. We derived the modified fo…
It has previously been shown that it is more general to describe the evolution of the universe based on the emergence of the space and the energy balance relation. Here we investigate the thermodynamic properties of the universe described by such a model. We show that the first law of thermodynamics and the generalized second law of thermodynamics (GSLT) are both satisfied and the weak energy condition are also fulfilled for two typical examples. Finally we examine the physical consistency for the present model.
It has shown that the accelerated expansion of the FRW Universe can be explained as the quest towards the holographic equipartition ($N_{sur} = N_{bulk}$), satisfies the expansion law $\frac{dV}{dt} = l_{P}^{2} \left( N_{sur} - εN_{bulk} \right)$, from which one can derive the Friedmann equation of the FRW Universe in Einstein gravity \cite{paddy2012jun}. We introduce a generic derivation of the expansion law from the generalized first law of thermodynamics $-dE=TdS$ and $dE=TdS + WdV$. The generic derivation provides an expression for $N_{sur}$ in terms of entropy $S$ and the expansion law co…
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.
We investigate the validity of the generalized second law in irreversible thermodynamics in a non-flat FRW universe containing the interacting dark energy with cold dark matter. The boundary of the universe is assumed to be enclosed by the dynamical apparent horizon. We show that for the present time, the generalized second law in nonequilibrium thermodynamics is satisfied for the special range of the energy transfer constants.
We derive a unified expansion law for our universe from the first law of thermodynamics on the apparent horizon, where entropic evolution depicts the emergence of cosmic space. The derivation advances a general form for degrees of freedom on the surface and bulk, which provides a natural generalization for the expansion law proposed by Padmanabhan. The general expression for the surface degrees of freedom differs from the natural expectation, $ N_{sur }= 4S $ in the emergent gravity paradigm for general theories of gravity. The derivation also provides justification for the selection of Gibbon…
Researches in the several decades have shown that the dynamics of gravity is closely related to thermodynamics of the horizon. In this paper, we derive the Friedmann acceleration equation based on the idea of "emergence of space" and thermodynamics of the Hubble horizon whose temperature is obtained from the unified first law of thermodynamics. Then we derive another evolution equation of the universe based on the energy balance relation $ρV_{H}=TS$. Combining the two evolution equations and the equation of state of the cosmic matter, we obtain the evolution solutions of the FRW universe. We f…
The present work aims to explore the model given by Lanczos-Lovelock gravity theories indexed by a fixed integer to require a unique anti-de Sitter vacuum, dressed by a scalar field non-minimal coupling. For this model, we add a special matter source characterized by a non-linear Maxwell field coupling with a function depending on the scalar field. Computing its thermodynamics parameters by using the Euclidean action, we obtain interesting and non zero thermodynamical quantities, unlike its original version, allowing analyzing thermodynamical stability. Together with the above, we found that t…
In the present paper, we are considering a spatially-flat Friedmann-Robertson-Walker cosmological model, fueled with stiff matter and dust, treated as non-interacting ideal fluid sources. By solving the corresponding Friedmann equation with a non-zero cosmological constant, we are deriving the scale function and the fundamental cosmological parameters. Within a thermodynamic approach, the general form of the Equation of State is obtained, together with the explicit dependence of the energy density and pressure on temperature.
The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein-Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.
Motivated by recent results on non-vanishing spatial curvature \cite{curve} we employ the holographic model of dark energy to investigate the validity of first and second laws of thermodynamics in non-flat (closed) universe enclosed by apparent horizon $R_A$ and the event horizon measured from the sphere of horizon named $L$. We show that for the apparent horizon the first law is roughly respected for different epochs while the second laws of thermodynamics is respected while for $L$ as the system's IR cut-off first law is broken down and second law is respected for special range of decelerati…
Author of Ref. [1], M.R. Setare (JCAP 01, 023, 2007, arXiv:hep-th/0701242), by redefining the event horizon measured from the sphere of the horizon as the system's IR cut-off for an interacting holographic dark energy model in a non-flat universe, showed that the generalized second law of thermodynamics is satisfied for the special range of the deceleration parameter. His paper includes an erroneous calculation of the entropy of the cold dark matter. Also there are some missing terms and some misprints in the equations of his paper. Here we present that his conclusion is not true and the gener…
We present a novel derivation of Einstein equations from the balance between Clausius entropy crossing the boundary of a local causal diamond and entanglement entropy associated with its horizon. Comparing this derivation with the entanglement equilibrium approach developed by Jacobson, we are able to argue for the equivalence of matter entanglement and Clausius entropy in the semiclassical regime. We also provide a direct comparison of both entropies for conformal matter, showing their equivalence without appealing to gravitational dynamics. Furthermore, we determine that gravitational dynami…
Padmanabhan in his paper [arxiv: 1206.4916] put forth an intriguing idea arguing that the accelerated expansion of the universse can be viewed as the emergence of cosmic space as cosmic time progresses, with the expansion triggered due to the difference in the degrees of freedom on a holographic surface and the one in its emerged bulk. We show that the modified expansion law of the universe proposed by Sheykhi in a non-flat Friedmann- Robertson-Walker (FRW) universe and by Cai in a flat FRW universe could be derived starting from the first law of thermodynamics, in (n+1) dimensional Einstein g…
We investigate the derivation of Friedmann equations in Rainbow gravity following Jacobson thermodynamic approach. We do not restrict the rainbow functions to be constant as is customarily used, and show that the first law of thermodynamics with a corresponding `classical' proportionality between entropy and surface area, supplemented eventually by a `quantum' logarithmic correction, are not in general sufficient to obtain the equations in flat FRW metrics.
It is known that static and spherically symmetric black hole solutions of general relativity in different spacetimes can be embedded into higher dimensional flat spacetime. Given this result, we have explored the thermodynamic nature of black holes á la its embedding into flat spacetime. In particular, we have explicitly demonstrated that black hole temperature can indeed be determined starting from the embedding and hence mapping of the static observers in black hole spacetime to Rindler observers in flat spacetime. Furthermore, by considering the dynamics of a scalar field in the flat spacet…
We study thermodynamics of (1+1) dimensional dilatonic black holes in global embedding Minkowski space scheme. Exploiting geometrical entropy correction we construct consistent entropy for the charged dilatonic black hole. Moreover, (1+1) dilatonic black holes with higher order terms are shown to possess (3+2) global flat embedding structures regardless of the details of the lapse function, and to yield a generic entropy.
Geometry of the universe has always intrigued mathematicians and cosmologists. Recent results from the Wilkinson Microwave Anisotropy Project (WMAP) indicate that the visible universe is incredibly flat. This apparent flatness could be due to the fact that only a small part of the universe is visible, thus indicating that the geometry of the universe is still an open and an interesting problem in cosmology. Assuming a profound connection between Friedmann, Robertson, Walker (FRW) geometries and thermodynamics, we construct a parameter free exploratory model that allows us to predict the geomet…
It was confirmed that the negative modes of the Euclidean section for asymptotically flat black holes reveal the thermodynamic instability of these black holes in the grand canonical ensemble (GCE). These include Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman black holes. In this work, we develop the relation between thermodynamic instability in the GCE and tachyonic instability for asymptotically flat black holes, where the latter is the onset for obtaining black holes with scalar hair. This implies that the tachyonic instability of black holes when introducing scalar coupling to th…
We derive non-flat cosmological models for two cases (i.e., dust and radiation) in the context of Møller's tetradic theory (MTT) of gravitation using the tetrad that creates the non-flat Friedmann-Robertson-Walker (FRW) metric. These two models are affected by the free dimensional parameter, $λ$, that characterized MTT, which approaches zero in the flat case for both models. Using standard definitions of thermodynamics, we calculate the radius horizon, Hawking temperature, and entropy of our non-flat models in the framework of cosmology and show the effect of $λ$ on open and closed universes. …
Discovery of a novel thermodynamic aspect of nonrelativistic gravity is reported. Here, initially, an unspecified scalar field potential is considered and treated not as an externally applied field but as a thermodynamic variable on an equal footing with the fluid variables. It is shown that the second law of thermodynamics imposes a stringent constraint on the field, and, quite remarkably, the allowable field turns out to be only of gravity. The resulting field equation for the gravitational potential derived from the analysis of the entropy production rate contains a dissipative term due to …
The spatial expansion of the universe can be described as the emergence of space with the progress of cosmic time, through a simple equation, $ΔV = Δt\left(N_{surf}- N_{bulk}\right)$. This law of emergence suggested by Padmanabhan in the context of general relativity for a flat universe has been generalized by Sheykhi to Gauss Bonnet and Lovelock gravity for a universe with any spacial curvature. We investigate whether this generalized holographic equipartition effectively implies the maximization of horizon entropy. First, we obtain the constraints imposed by the maximization of horizon entro…
There ought to exist a description of quantum field theory which does not depend on an external classical time. To achieve this goal, in a recent paper we have proposed a non-commutative special relativity in which space-time and matter degrees of freedom are treated as classical matrices with arbitrary commutation relations, and a space-time line element is defined using a trace. In the present paper, following the theory of Trace Dynamics, we construct a statistical thermodynamics for the non-commutative special relativity, and show that one arrives at a generalized quantum dynamics in which…
Asymptotically-flat Black holes in Bumblebee gravity: Exact solutions and Thermodynamics
Guangzhou University（广州大学）；Guangxi University（广西大学）；Southern Medical University（南方医科大学）；Peking University（北京大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
The phase structure and critical phenomena of the 3+1 dimensional charged black holes in asymptotically flat spacetime are investigated in terms of thermodynamic properties within the Rényi statistics. With this approach as the non-extensive parameter above zero, we find that the charged black hole can be in thermodynamic equilibrium with surrounding thermal radiation, and have a Hawking-Page phase transition in the same way in the case of AdS charged black hole. This gives more evidence supporting the proposal that there exists an equivalence between the black hole thermodynamics in asymptoti…
Motivated by the string corrections on the gravity and electrodynamics sides, we consider a quadratic Maxwell invariant term as a correction of the Maxwell Lagrangian to obtain exact solutions of higher dimensional topological black holes in Gauss-Bonnet gravity. We first investigate the asymptotically flat solutions and obtain conserved and thermodynamic quantities which satisfy the first law of thermodynamics. We also analyze thermodynamic stability of the solutions by calculating the heat capacity and the Hessian matrix. Then, we focus on horizon-flat solutions with adS asymptote and produc…
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…
Our primary goal in this paper is to confirm new universal relations in black hole thermodynamics. We investigate the universal relations by selecting different black holes. First, we obtain the black holes' thermodynamic relations assuming a new minor correction is added to the AdS part of the action. Then we confirm the universal relations by performing a series of direct calculations. It is noteworthy that according to each of the properties related to black holes, a new universal relation can be obtained according to this method. We confirm two different types of these universal relations …
We analyse in detail the thermodynamics in the canonical and grand canonical ensembles of a class of non-asymptotically flat black holes of the Einstein-(anti) Maxwell-(anti) Dilaton theory in 4D with spherical symmetry. We present the first law of thermodynamics, the thermodynamic analysis of the system through the geometrothermodynamics methods, Weinhold, Ruppeiner, Liu-Lu-Luo-Shao and the most common, that made by the specific heat. The geometric methods show a curvature scalar identically zero, which is incompatible with the results of the analysis made by the non null specific heat, which…
The Hessian of the entropy function can be thought of as a metric tensor on state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study these geometries for some families of black holes and find that the Ruppeiner geometry is flat for Reissner--Nordström black holes in any dimension, while curvature singularities occur for the Kerr black holes. Kerr black holes have instead flat Weinhold curvature.
Motivated by the recent work of Wang, Lin, Pavon, and Abdalla [1], we generalize their work to the non-flat case. In particular, we provide a thermodynamical interpretation for the holographic dark energy model in a non-flat universe. For this case, the characteristic length is no more the radius of the event horizon (R_E) but the event horizon radius as measured from the sphere of the horizon (L). Furthermore, when interaction between the dark components of the holographic dark energy model in the non-flat universe is present its thermodynamical interpretation changes by a stable thermal fluc…
The numerical study indicates that there exists a relation between the quasinormal modes and the Davies point for a black hole. In this paper, we analytically study this relation for the charged Reissner-Nordström black holes in asymptotically flat and dS spacetimes. In the eikonal limit, the angular velocity $Ω$ and the Lyapunov exponent $λ$ of the photon sphere, respectively, corresponding to the real and imaginary parts of the quasinormal modes are obtained from the null geodesics. Both in asymptotically flat and dS spacetimes, we observe the spiral-like shapes in the complex quasinormal mo…
We analyze the structural and thermodynamic properties of $D$-dimensional ($D \geq 4$), asymptotically flat or Anti-de-Sitter, electrically charged black hole solutions, resulting from the minimal coupling of general nonlinear electrodynamics to General Relativity. This analysis deals with static spherically symmetric (elementary) configurations with spherical horizons. Our methods are based on the study of the behaviour (in vacuum and on the boundary of their domain of definition) of the Lagrangian density functions characterizing the nonlinear electrodynamic models in flat spacetime. These f…
It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective. The virtual degrees of freedom associated with the horizons perceived by the local Rindler observers, play a crucial role in this approach. In this context, the relation S=E/2T between the entropy (S), active gravitational mass (E) and temperature (T) - obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] - can be reinterpreted as the law of equipartition E = (1/2) nkT where n=A/L_P^2 is the number (density) of microscopic horizon degrees of freedom. Conversely,…
We explain flat rotation curves and the baryonic Tully-Fisher relation by a combination of three hypotheses. The first is a formulation of the equivalence principle for gravitationally bound quantum $N$ body systems, while the second is a second order phase transition hypothesized to arise from a competition between the effects of Unruh and deSitter radiation experienced by a static observer in a galaxy. The third is a light dark matter particle, coupled to a dark photon. The phase transition is triggered in a ring where the Unruh temperature of a static observer falls below the deSitter tempe…
Microphysical laws are time reversible, but macrophysics, chemistry and biology are not. This chapter explores how this asymmetry (a classic example of a broken symmetry) arises due to the cosmological context, where a non-local Direction of Time is imposed by the expansion of the universe. This situation is best represented by an Evolving Block Universe, where local arrows of time (thermodynamic, electrodynamic, gravitational, wave, quantum, biological) emerge in concordance with the Direction of Time because a global Past Condition results in the Second Law of Thermodynamics pointing to the …
The present study is motivated by the study of reference [1], where the generalized second law of thermodynamics has been investigated for a flat FRW universe for two viable models of $f(T)$ gravity. In the present work, we have considered a non-flat universe and accordingly studied the behaviors of equation of state parameter and deceleration parameter. Subsequently, using the first law of thermodynamics we derived the expressions for the time derivative of the total entropy of a universe enveloped by apparent horizon. In the next phase, with the choice of scale factor pertaining to an emerge…
In this paper we will show that using the cosmological constant as a new thermodynamical state variable, the differential and integral mass formulas of the first law of thermodynamics for asymptotic flat spacetimes can be extended to (2+1) dimensional charged BTZ black holes and charged de Sitter space.
Authors of ref. [1], M.R. Setare and S. Shafei (JCAP 09 (2006) 011), studied the thermodynamics of a holographic dark energy model in a non-flat universe enclosed by the apparent horizon $R_A$ and the event horizon measured from the sphere of the horizon named $L$. In section 3 in ref. [1], Authors showed that for $R_A$ the generalized second law of thermodynamics is respected, while for $L$ it is satisfied for the special range of the deceleration parameter. Here we present that their calculations for $R_A$ should be revised. Also we show that their conclusion for $L$ is not true and the gene…
We present Friedmann flat spacetime uncertainty relations (STUR) together with some cosmological implications. An interesting link between the Principle of "gravitational stability against localization of events" (PGSL) and the holographic Bekenstein entropy bound (HEB) is also investigated. The same theorems leading to our STUR are used to calculate, thanks to the holographic principle, the entropy of the universe at its apparent horizon. The generalized entropy formula can be used to discuss interesting links with a quantum spacetime.
We present an investigation on thermodynamics of two different types of black holes viz. Kiselev black hole (asymptotically flat) and Taub-NUT (non-asymptotically flat) black hole. We compute the thermodynamic variables like black hole's Hawking temperature, entropy at the black hole's event horizon. Further we derive the heat capacity and examine it to study the thermal stability of the black holes. We also calculate the rate of emission assuming the black holes radiate energy in terms of photons by tunneling. We represent all the parameters including the rate of emission of the black holes g…
Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law of thermodynamics applied to local holographic screens. This is accomplished by essentially reversing the steps of Hawking's area theorem, leading to the Ricci convergence condition as an input, from which an application of Einstein's equations yields the NEC -- even in the presence of 1-loop quantum corrections to the Bekenstein-Hawking entropy formula. Then, by attributing thermodynamics to the stretche…
We investigate the thermodynamics of Einstein-Maxwell(-Dilaton) theory for an asymptotically flat spacetime in a quasilocal frame. We firstly define a quasilocal thermodynamic potential via the Euclidean on-shell action and formulate a quasilocal Smarr relation from Eulerian theorem. Then we calculate quasilocal energy and surface pressure by employing Brown-York quasilocal method along with Mann-Marolf counterterm and find entropy from the quasilocal thermodynamic potential. These quasilocal variables are consistent with Tolman temperature and the entropy in a quasilocal frame turns out to be…
There are various reasons to believe that quantum theory could be an emergent phenomenon. Trace Dynamics is an underlying classical dynamics of non-commuting matrices, from which quantum theory and classical mechanics have been shown to emerge, in the thermodynamic approximation. However, the time that is used to describe evolution in quantum theory is an external classical time, and is in turn expected to be an emergent feature - a relic of an underlying theory of quantum gravity. In this essay we borrow ideas from Trace Dynamics to show that classical time is a thermodynamic approximation to…
We study the thermodynamics of the KS black hole which is an asymptotically flat solution of the HL gravity. In particular, we introduce a cavity to describe the thermodynamics at a finite isothermal surface on general ground and to get a well-defined thermodynamics. We show that there exists a locally stable small black hole which tunnels to the hot flat space below the critical temperature and to the large black hole above the critical temperature. Moreover, it turns out that the remnant decays into the vacuum through a quantum tunneling.
The thermodynamics of three-dimensional asymptotically flat cosmological solutions that play the same role than the BTZ black holes in the anti-de Sitter case is derived and explained from holographic properties of flat space. It is shown to coincide with the flat-space limit of the thermodynamics of the inner black hole horizon on the one hand and the semi-classical approximation to the gravitational partition function associated to the entropy of the outer horizon on the other. This leads to the insight that it is the Massieu function that is universal in the sense that it can be computed at…
