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

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 $T_hd\hat{S}_h=δ{Q}$, where $δ{Q}=-d\hat{E}+Wd\mathbb{V}+T_hd_{\jmath}\hat{S}$ 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.

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