Unified First Law Of Thermodynamics Research Articles

Unified first law of thermodynamics in Gauss–Bonnet gravity on an FLRW background

Unified first law of thermodynamics in Gauss–Bonnet gravity on an FLRW background

Holographic vacuum energy regularization and corrected entropy of de Sitter space

Abstract We propose that the spectrum of the surface area of the apparent horizon (AH) of de Sitter (dS) spacetime leads to corrected temperature and entropy of the dS spacetime, offering new insights into its thermodynamic properties. This is done by employing the spectrum of the AH radius, acquired from the Wheeler--DeWitt (WDW) equation, together with the Stefan--Boltzmann law, the time-energy uncertainty relation, and the unified first law of thermodynamics.

Amended FRW universe: thermodynamics and heat engine

Thermodynamics of non-flat Amended Friedmann–Robertson–Walker (AFRW) universe with cosmological constant as thermodynamic pressure is studied. The unified first law of thermodynamics, the Clausius relation and the gravity equations yield entropy on the dynamic apparent horizon. Temperature, volume, pressure, enthalpy, Gibb’s free energy and Helmholtz’s free energies, and specific heat capacity with constant pressure of the universe are calculated in terms of surface area of dynamic apparent horizon. The study shows a non-negative Joule–Thomson coefficient, indicating the cooling nature of the AFRW universe. Inversion pressure and inversion temperature are expressed in terms of the surface area of the apparent horizon. Finally, the thermodynamical AFRW universe is considered as a heat engine. Work done for the Carnot engine is derived with maximum efficiency, and a new engine is also considered for which the work done, and its efficiency are calculated for AFRW universe.

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

Modified cosmology from quantum deformed entropy

Jalalzadeh (2022), established that the thermodynamical entropy of a quantum-deformed black hole with horizon area A can be written as Sq=πsinA8GN/sinπ2N, where N=Lq2/LP2, LP being the Planck length and Lq denoting, generically, the q-deformed cosmic event horizon distance Lq. Motivated by this, we now extend the framework constructed in Jalalzadeh (2022) towards the Friedmann and Raychaudhuri equations describing spatially homogeneous and isotropic universe dynamics. Our procedure in this paper involves a twofold assumption. On the one hand, we take the entropy associated with the apparent horizon of the Robertson–Walker universe in the form of the aforementioned expression. On the other hand, we assume that the unified first law of thermodynamics, dE=TdS+WdV, holds on the apparent horizon. Subsequently, we find a novel modified cosmological scenario characterized by quantum-deformed (q-deformed) Friedmann and Raychaudhuri equations containing additional components that generate an effective dark energy sector. Our results indicate an effective dark energy component, which can explain the Universe’s late-time acceleration. Moreover, the Universe follows the standard thermal history, with a transition redshift from deceleration to acceleration at ztran=0.5. More precisely, according to our model, at a redshift of z=0.377, the effective dark energy dominates with a de Sitter universe in the long run. We include the evolution of luminosity distance, μ, the Hubble parameter, H(z), and the deceleration parameter, q(z), versus redshift. Finally, we have conducted a comparative analysis of our proposed model with others involving non-extensive entropies.

Emergence of cosmic space and its connection with thermodynamic principles

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 correctly reproduces the standard evolution of a Friedmann universe. We establish the connection of the law of emergence, which is conceptually different from the conventional paradigm to describe cosmology, with other well-established results in thermodynamics. It has been shown that the law of emergence can be derived from the unified first law of thermodynamics, which can then be considered as the backbone of the law. However, the law of emergence is rich in structure than implied by the First law thermodynamics alone. It further explains the evolution of the universe towards a state of maximum horizon entropy. Following this, it can be considered that the first law of thermodynamics, along with the additional constraints imposed by the maximisation of the horizon entropy, can together lead to the law of emergence. In the present article, we first make a brief review of Padmanabhan's proposal and then studies its connection with the thermodynamics of the horizon in the context of Einstein's, Gauss-Bonnet, and more general Lovelock gravity theories.

Thermodynamics of dynamical wormholes

We study thermodynamics of dynamical traversable wormholes. The surface gravity is evaluated on the trapping horizon and the unified first law of thermodynamics is set up. The thermodynamic stability of these wormholes has been investigated. We have also extended these results to charged dynamical wormholes. Our results generalize those that exist for static Morris-Thorne wormholes.

Generalized Misner–Sharp energy in generalized Rastall theory

Employing the unified first law of thermodynamics and the field equations of the generalized Rastall theory, we get the generalized Misner–Sharp mass of space–times for which gtt = –grr = –f(r). The obtained result differs from those of the Einstein and Rastall theories. Moreover, using the first law of thermodynamics, the obtained generalized Misner–Sharp mass, and the field equations, the entropy of static spherically symmetric horizons are also addressed in the framework of the generalized Rastall theory. In addition, by generalizing the study to a flat Friedmann–Robertson–Walker (FRW) universe, the apparent horizon entropy is also calculated. Considering the effects of applying the Newtonian limit to the field equations on the coupling coefficients of the generalized Rastall theory, our study indicates (i) the obtained entropy–area relation is the same as that of the Rastall theory, and (ii) the Bekenstein entropy is recovered when the generalized Rastall theory reduces to the Einstein theory. The validity of the second law of thermodynamics is also investigated in the flat FRW universe.

Unified first law for traversable wormholes in non-minimal coupling of curvature and matter

In this paper thermodynamics of static Morris–Thorne wormholes has been discussed in the context of f(R) gravity. The generalized surface gravity, unified first law of thermodynamics and wormhole dynamics have been studied at trapping horizons. We have investigated thermodynamics in non-minimal coupling of curvature and matter which produces very complex equations. Our results generalize the results that have already been derived in Einstein’s gravity in the absence of curvature–matter coupling.

Unified first law in inhomogeneous and anisotropic spacetime models: Some general prescription

In this paper we investigate the interrelationship between the unified first law of thermodynamics and the Friedmann equations for three anisotropic and inhomogeneous spacetime metrics namely Lemaître–Tolman–Bondi and Friedmann–Lemaître–Robertson–Walker type inhomogeneous spacetime model and Kantowski–Sachs type model. In all these models we find that Einstein field equations are obtained by projecting the unified first law along and perpendicular to the Kodama vector and also along two linearly independent directions.

Accelerated expansion of the universe based on emergence of space and thermodynamics of the horizon

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 ρVH=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 find that the solutions obtained by us include the solutions obtained in the standard general relativity (GR) theory. Therefore, it is more general to describe the evolution of the universe in the thermodynamic way.

Thermodynamic Analysis of Gravitational Field Equations in Lyra Manifold

Considering the Einstein field equations in Lyra manifold and applying the unified first law of thermodynamics as well as the Clausius relation to the apparent horizon of FRW universe, we find the entropy of apparent horizon in Lyra manifold. In addition, the validity of second law of thermodynamics and its generalized form are also studied. Finally, we use the first law of thermodynamics in order to find the horizon entropy of static spherically symmetric spacetimes. Some results of considering (anti)de-Sitter and Schwarzschild metrics have also been addressed.

Implications, Consequences and Interpretations of Generalized Entropy in the Cosmological Setups

Recently, it was argued (Eur. Phys. J. C {\bf73}, 2487 (2013)) that the total entropy of a gravitational system should be related to the volume of system instead of the system surface. Here, we show that this new proposal cannot satisfy the unified first law of thermodynamics and the Friedmans equation simultaneously, unless the effects of dark energy candidate on the horizon entropy are considered. In fact, our study shows that some types of dark energy candidate may admit this proposal. Some general properties of required dark energy are also addressed. Moreover, our investigation shows that this new proposal for entropy, while combined with the second law of thermodynamics (as the backbone of Verlinde's proposal), helps us in providing a thermodynamic interpretation for the difference between the surface and bulk degrees of freedom which, according to Padmanabhan's proposal, leads to the emergence of spacetime and thus the universe expansion. In fact, our investigation shows that the entropy changes of system may be equal to the difference between the surface and bulk degrees of freedom falling from surface into the system volume. Briefly, our results signal us that this new proposal for entropy may be in agreement with the thermodynamics laws, the Friedmann equation, Padmanabhan's holographic proposal for the emergence of spacetime and therefore the universe expansion. In fact, this new definition of entropy may be used to make a bridge between Verlinde's and Padmanabhan's proposals.

Thermodynamical Study of FRW Universe in Quasi-Topological Theory

By applying the unified first law of thermodynamics on the apparent horizon of FRW universe, we get the entropy relation for the apparent horizon in quasi-topological gravity theory. Throughout the paper, the results of considering the Hayward-Kodama and Cai-Kim temperatures are also addressed. Our study shows that whenever there is no energy exchange between the various parts of cosmos, we can get an expression for the apparent horizon entropy in quasi-topological gravity, which is in agreement with other attempts that followed different approaches. The effects of a mutual interaction between the various parts of cosmos on the apparent horizon entropy as well as the validity of second law of thermodynamics in quasi-topological gravity are perused.

Thermodynamic Analysis of the Static Spherically Symmetric Field Equations in Rastall Theory

The restrictions on the Rastall theory due to application of the Newtonian limit to the theory are derived. In addition, we use the zero-zero component of the Rastall field equations as well as the unified first law of thermodynamics to find the Misner-Sharp mass content confined to the event horizon of the spherically symmetric static spacetimes in the Rastall framework. The obtained relation is calculated for the Schwarzschild and de-Sitter back holes as two examples. Bearing the obtained relation for the Misner-Sharp mass in mind together with recasting the one-one component of the Rastall field equations into the form of the first law of thermodynamics, we obtain expressions for the horizon entropy and the work term. Finally, we also compare the thermodynamic quantities of system, including energy, entropy, and work, with their counterparts in the Einstein framework to have a better view about the role of the Rastall hypothesis on the thermodynamics of system.

Thermodynamics of universe with a varying dark energy component

We consider a Friedmann–Robertson–Walker (FRW) universe filled by a dark energy (DE) candidate together with other possible sources which may include the baryonic and nonbaryonic matters. Thereinafter, we consider a situation in which the cosmos sectors do not interact with each other. By applying the unified first law of thermodynamics on the apparent horizon of the FRW universe, we show that the DE candidate may modify the apparent horizon entropy and thus the Bekenstein limit. Moreover, we generalize our study to the models in which the cosmos sectors have a mutual interaction. Our final result indicates that the mutual interaction between the cosmos sectors may add an additional term to the apparent horizon entropy leading to modify the Bekenstein limit. Relationships with previous works have been addressed throughout the paper. Finally, we investigate the validity of the second law of thermodynamics and its generalized form in the interacting and noninteracting cosmoses.

A study of universal thermodynamics in massive gravity: modified entropy on the horizons

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.

Thermodynamics of the Apparent Horizon in FRW Universe with Massive Gravity

Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation δQ = T d S, where the heat Bow δQ is the energy-supply of pure matter projecting on the vector ξ tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/(2πr̃A), the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit Hc → 0, which recovers the Minkowski reference metric solution in the fiat case, the generalized second law of thermodynamics holds if α3 + 4α4 < 0. Without this condition, even for the simplest model of dRGT massive cosmology with α3 = α4 = 0, the generalized second law of thermodynamics could be violated.

Thermodynamics of Lema $$\hat{i}$$ tre−Tolman−Bondi Model

Here we consider our universe as inhomogeneous spherically symmetric Lemaitre-Tolman-Bondi Model and analyze the thermodynamics of this model of the universe. The trapping horizon is calculated and is found to coincide with the apparent horizon. The Einstein field equations are shown to be equivalent with the unified first law of thermodynamics. Finally assuming the first law of thermodynamics validity of the generalized second law of thermodynamics is examined at the apparent horizon for the perfect fluid and at the event horizon for holographic dark energy.

HAWKING RADIATION AS TUNNELING AND THE UNIFIED FIRST LAW OF THERMODYNAMICS FOR A CLASS OF DYNAMICAL BLACK HOLES

An analysis is made for relations between the tunneling rate and the unified first law of thermodynamics at the trapping horizons of two kinds of spherically symmetric dynamical black holes. The first kind is the Vaidya–Bardeen black hole; the tunneling rate Γ ~ e△S can be obtained naturally from the unified first law at the apparent horizon, which holds the form dEH = TdS + WdV. The second kind is the McVittie solution; the action of the radial null geodesic of the outgoing particles does not always have a pole at the apparent horizon, while the ingoing mode always has one. The solution of the ingoing mode of the radiation can be mathematically reduced to the case in the FRW universe smoothly. However, as a black hole, the physical meaning is unclear and even puzzling.