Thermodynamics of apparent horizon and modified Friedman equations

TL;DR

This paper derives modified Friedmann equations for a FRW universe using quantum-corrected entropy at the apparent horizon and confirms the generalized second law of thermodynamics holds under these conditions.

Contribution

It introduces a quantum-corrected entropy relation into the thermodynamic derivation of Friedmann equations for any spatial curvature.

Findings

Modified Friedmann equations incorporating quantum entropy corrections.

Validation that the generalized second law of thermodynamics is satisfied.

Analysis of entropy evolution including matter and horizon contributions.

Abstract

Starting from the first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon of a FRW universe, and assuming that the associated entropy with apparent horizon has a quantum corrected relation, $S=\frac{A}{4G}-\alpha \ln \frac{A}{4G}+\beta \frac{4G}{A}$, we derive modified Friedmann equations describing the dynamics of the universe with any spatial curvature. We also examine the time evolution of the total entropy including the quantum corrected entropy associated with the apparent horizon together with the matter field entropy inside the apparent horizon. Our study shows that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.