Thermodynamics in f(R,T) Theory of Gravity

TL;DR

This paper explores the thermodynamic behavior at the apparent horizon of the FRW universe within $f(R,T)$ gravity, revealing non-equilibrium features and confirming the validity of the second law of thermodynamics.

Contribution

It demonstrates that equilibrium thermodynamics is not achievable in $f(R,T)$ gravity and reformulates Friedmann equations as a thermodynamic first law with entropy production.

Findings

Thermodynamics at the apparent horizon is non-equilibrium in $f(R,T)$ gravity.

The first law of thermodynamics is valid with an entropy production term.

The second law of thermodynamics holds in both phantom and non-phantom phases.

Abstract

A non-equilibrium picture of thermodynamics is discussed at the apparent horizon of FRW universe in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. We take two forms of the energy-momentum tensor of dark components and demonstrate that equilibrium description of thermodynamics is not achievable in both cases. We check the validity of the first and second law of thermodynamics in this scenario. It is shown that the Friedmann equations can be expressed in the form of first law of thermodynamics $T_hdS'_h+T_hd_{\jmath}S'=-dE'+W'dV$, where $d_{\jmath}S'$ is the entropy production term. Finally, we conclude that the second law of thermodynamics holds both in phantom and non-phantom phases.