Thermodynamics in $f(R)$ gravity in the Palatini formalism

TL;DR

This paper explores the thermodynamics of the apparent horizon in $f(R)$ gravity within the Palatini formalism, comparing equilibrium and non-equilibrium descriptions, and verifies the second law of thermodynamics in different cosmic phases.

Contribution

It clarifies the thermodynamic behavior of $f(R)$ gravity in the Palatini formalism, emphasizing the advantages of the equilibrium framework over the non-equilibrium one.

Findings

Equilibrium description provides clearer understanding of horizon entropy.

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

Thermodynamic analysis is consistent with universe temperature continuity.

Abstract

We investigate thermodynamics of the apparent horizon in $f(R)$ gravity in the Palatini formalism with non-equilibrium and equilibrium descriptions. We demonstrate that it is more transparent to understand the horizon entropy in the equilibrium framework than that in the non-equilibrium one. Furthermore, we show that the second law of thermodynamics can be explicitly verified in both phantom and non-phantom phases for the same temperature of the universe outside and inside the apparent horizon.