Thermodynamic properties of modified gravity theories

TL;DR

This paper reviews the thermodynamic properties of modified gravity theories like $F(R)$ and $f(T)$ gravity, exploring their thermodynamic equivalences and implications for the universe's second law.

Contribution

It demonstrates the thermodynamic equivalence of equations of motion in modified gravity and explores horizon thermodynamics in both equilibrium and non-equilibrium frameworks.

Findings

Equivalence between modified gravity equations and thermodynamic relations.

Thermodynamics of the cosmological apparent horizon in $f(T)$ gravity.

Second law of thermodynamics holds when horizon temperatures are equal.

Abstract

We review thermodynamic properties of modified gravity theories such as $F(R)$ gravity and $f(T)$ gravity, where $R$ is the scalar curvature and $T$ is the torsion scalar in teleparallelism. In particular, we explore the equivalence between the equations of motion for modified gravity theories and the Clausius relation in thermodynamics. In addition, thermodynamics of the cosmological apparent horizon is investigated in $f(T)$ gravity. We show both equilibrium and non-equilibrium descriptions of thermodynamics. It is demonstrated that the second law of thermodynamics in the universe can be met when the temperature of the outside of the apparent horizon is equivalent to that of the inside of it.