Thermodynamic descriptions of polytropic gas and its viscous type as dark energy candidates

Abstract

In this paper, at first, we focus on a FRW universe in which the dark energy candidate satisfies the Polytropic equation of state and study thermodynamics of dark energy. Bearing the thermal fluctuation theorem in mind, we establish a relation between the thermal fluctuation of system and mutual interaction between the dark energy and dark matter. Generalization to a viscous Polytropic gas is also investigated. We point to a condition for decaying dark energy candidate into the dark matter needed for alleviating coincidence problem. The effects of dark energy candidates and their interactions with other parts of cosmos on the horizon entropy as well as the second law of thermodynamics are also addressed. Our study signals us to a correction term besides the Bekenstein entropy which carries the information of the dark energy candidate, its interaction with other parts of cosmos and its viscosity.

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

“…It is useful to note here that although the Bekenstein entropy is in line with the current accelerating phase of universe expansion and the second and generalized second laws of thermodynamics [17,18], some authors show that a dark energy candidate, due to its unknown nature, may modify the horizon entropy (the Bekenstein limit in the Einstein general relativity framework) [19][20][21][22][23]. In their setups, the Friedmann equation and the second law of thermodynamics are still valid simultaneously [19][20][21][22][23]. Finally, it is useful to mention here that one may get the universe evolution equation in various theories of gravity (the corresponding Friedmann equation), by taking into account the horizon entropy relation together with the Hayward-Kodama temperature and applying the unified first law of thermodynamics on the apparent horizon of FLRW universe [24].…”

“…Now, since there are some works showing that a dark energy candidate may modify the horizon entropy [19][20][21][22][23], can one make a relation between the energy density of dark energy candidate and the general entropy relation? Here, we are going to investigate the possibility of establishing a relation between these attempts and the generalized entropy proposed by Tsallis et al [54], which is also supported by the quantum cosmology considerations [55].…”

“…in that S A is the horizon entropy, and mines sign comes from the universe expansion [9,10,[21][22][23]. Now, for a theory in which S A = S A (A), since the Cai-Kim temperature meets the [9,10,15,16], one reaches…”

“…It was also argued that a dark energy candidate, due to its unknown nature, may modify the apparent horizon entropy in various theories of gravity [19][20][21][22][23]. In fact, by decomposing ρ to ρ D +ρ o , in which ρ D denotes the energy density of dark energy candidate and ρ o includes the energy density of other parts of cosmos, using the Friedman equation (10), continuity equation (4) together with the unified first law of thermodynamics and the Clausius relation, one can obtain a new relation for the horizon entropy as…”

Thermodynamic Analysis of Gravitational Field Equations in Lyra Manifold

“…for the horizon entropy [39][40][41][42][43][44]. Here, and denote the energy density and pressure components of ] , respectively.…”