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It is shown that adding hair like electric charge or angular momentum to the black hole decreases the amount of entropy emission. This motivates us to study the emission rate of entropy from black holes and conjecture a maximum limit (upper bound) on the rate of local entropy emission ($dot{S}$) for thermal systems in four dimensional space time and argue that this upper bound is $dot{S}simeq k_{B} sqrt{frac{c^5}{hbar G}}$. Also by considering R`{e}nyi entropy, it is shown that Bekenstein-Hawking entropy leads to a maximum limit for the rate of entropy emission. We also suggest an upper bound on the surface gravity of the black holes which is called Planck surface gravity. Finally we obtain a relation between maximum rate of entropy emission, Planck surface gravity and Planck temperature of black holes.
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Two maximization problems of Renyi entropy rate are investigated: the maximization over all stochastic processes whose marginals satisfy a linear constraint, and the Burg-like maximization over all stochastic processes whose autocovariance function begins with some given values. The solutions are related to the solutions to the analogous maximization problems of Shannon entropy rate.
Discrete formulations of (quantum) gravity in four spacetime dimensions build space out of tetrahedra. We investigate a statistical mechanical system of tetrahedra from a many-body point of view based on non-local, combinatorial gluing constraints that are modelled as multi-particle interactions. We focus on Gibbs equilibrium states, constructed using Jaynes principle of constrained maximisation of entropy, which has been shown recently to play an important role in characterising equilibrium in background independent systems. We apply this principle first to classical systems of many tetrahedra using different examples of geometrically motivated constraints. Then for a system of quantum tetrahedra, we show that the quantum statistical partition function of a Gibbs state with respect to some constraint operator can be reinterpreted as a partition function for a quantum field theory of tetrahedra, taking the form of a group field theory.
We consider a static self-gravitating perfect fluid system in Lovelock gravity theory. For a spacial region on the hypersurface orthogonal to static Killing vector, by the Tolmans law of temperature, the assumption of a fixed total particle number inside the spacial region, and all of the variations (of relevant fields) in which the induced metric and its first derivatives are fixed on the boundary of the spacial region, then with the help of the gravitational equations of the theory, we can prove a theorem says that the total entropy of the fluid in this region takes an extremum value. A converse theorem can also be obtained following the reverse process of our proof. We also propose the definition of isolation quasi-locally for the system and explain the physical meaning of the boundary conditions in the proof of the theorems.
We consider a static self-gravitating system consisting of perfect fluid with isometries of an $(n-2)$-dimensional maximally symmetric space in Lovelock gravity theory. A straightforward analysis of the time-time component of the equations of motion suggests a generalized mass function. Tolman-Oppenheimer-Volkoff like equation is obtained by using this mass function and gravitational equations. We investigate the maximum entropy principle in Lovelock gravity, and find that this Tolman-Oppenheimer-Volkoff equation can also be deduced from the so called maximum entropy principle which is originally customized for Einstein gravity theory. This investigation manifests a deep connection between gravity and thermodynamics in this generalized gravity theory.
In this work, we analyzed the effect of different prescriptions of the IR cutoffs, namely the Hubble horizon cutoff, particle horizon cutoff, Granda and Oliveros horizon cut off, and the Ricci horizon cutoff on the growth rate of clustering for the Tsallis holographic dark energy (THDE) model in an FRW universe devoid of any interactions between the dark Universe. Furthermore, we used the concept of configurational entropy to derive constraints (qualitatively) on the model parameters for the THDE model in each IR cutoff prescription from the fact that the rate of change of configurational entropy hits a minimum at a particular scale factor $a_{DE}$ which indicate precisely the epoch of dark energy domination predicted by the relevant cosmological model as a function of the model parameter(s). By using the current observational constraints on the redshift of transition from a decelerated to an accelerated Universe, we derived constraints on the model parameters appearing in each IR cutoff definition and on the non-additivity parameter $delta$ characterizing the THDE model and report the existence of simple linear dependency between $delta$ and $a_{DE}$ in each IR cutoff setup.
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