# Thermodynamics in $f\left(\mathcal{G},T\right)$ Gravity

Sharif, M.  (Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan) ; Ikram, Ayesha (Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan)

08 March 2018

Abstract: This paper explores the nonequilibrium behavior of thermodynamics at the apparent horizon of isotropic and homogeneous universe model in $f\left(\mathcal{G},T\right)$ gravity ( $\mathcal{G}$ and $T$ represent the Gauss-Bonnet invariant and trace of the energy-momentum tensor, resp.). We construct the corresponding field equations and analyze the first as well as generalized second law of thermodynamics in this scenario. It is found that an auxiliary term corresponding to entropy production appears due to the nonequilibrium picture of thermodynamics in first law. The universal condition for the validity of generalized second law of thermodynamics is also obtained. Finally, we check the validity of generalized second law of thermodynamics for the reconstructed $f\left(\mathcal{G},T\right)$ models (de Sitter and power-law solutions). We conclude that this law holds for suitable choices of free parameters.

Published in: Advances in High Energy Physics 2018 (2018) 2563871