Thermodynamics in Modified Gravity Theories

TL;DR

This paper shows that an equilibrium thermodynamic description exists on the apparent horizon in a broad class of modified gravity theories, simplifying the understanding of horizon entropy and energy conservation in cosmology.

Contribution

It introduces a suitable energy-momentum tensor for dark components in modified gravity, enabling an equilibrium thermodynamic framework on the apparent horizon.

Findings

Existence of equilibrium thermodynamics in modified gravity theories.

A new definition of energy-momentum tensor obeying local conservation.

Equilibrium description accounts for horizon entropy and entropy production.

Abstract

We demonstrate that there does exist an equilibrium description of thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density $f(R, \phi, X)$, where $R$ is the Ricci scalar and $X$ is the kinetic energy of a scalar field $\phi$. This comes from a suitable definition of an energy momentum tensor of the "dark" component obeying the local energy conservation law in the Jordan frame. It is shown that the equilibrium description in terms of the horizon entropy $S$ is convenient because it takes into account the contribution of the horizon entropy $\hat{S}$ in non-equilibrium thermodynamics as well as an entropy production term.