Thermodynamic Behavior of particular $f(R,T)$ Gravity Models

TL;DR

This paper explores the thermodynamic properties of $f(R,T)$ gravity models at the apparent horizon of the FRW universe, focusing on non-equilibrium thermodynamics and conditions for the second law to hold.

Contribution

It analyzes the thermodynamics of specific $f(R,T)$ gravity models, including the formulation of the first law and conditions for the generalized second law in a non-equilibrium setting.

Findings

First law expressed via Clausius relation with entropy production.

Conditions for the validity of the generalized second law established.

Results illustrated for concrete $f(R,T)$ models.

Abstract

We investigate the thermodynamics at the apparent horizon of the FRW universe in $f(R,T)$ theory under non-equilibrium description. The laws of thermodynamics have been discussed for two particular models of $f(R,T)$ theory. The first law of thermodynamics is expressed in the form of Clausius relation $T_hd\hat{S}_h=\delta{Q}$, where $\delta{Q}=-d\hat{E}+Wd\mathbb{V}+T_hd_{\jmath}\hat{S}$ is the energy flux across the horizon and $d_{\jmath}\hat{S}$ is the entropy production term. Furthermore, the conditions to preserve the generalized second law of thermodynamics are established with the constraints of positive temperature and attractive gravity. We have illustrated our results for some concrete models in this theory.