The generalized second law of thermodynamics in generalized gravity theories

TL;DR

This paper explores the validity of the generalized second law of thermodynamics across various gravity theories, deriving conditions under which the law holds and confirming its applicability in multiple models including Einstein, Lovelock, braneworld, $f(R)$, and scalar-tensor gravities.

Contribution

It derives a universal condition ensuring the validity of the GSL in generalized gravity theories and verifies this condition across several specific models.

Findings

GSL holds in Einstein, Lovelock, and braneworld gravities.

GSL can be protected in $f(R)$ and scalar-tensor gravities under certain conditions.

A universal condition for the GSL validity is established.

Abstract

We investigate the generalized second law of thermodynamics (GSL) in generalized theories of gravity. We examine the total entropy evolution with time including the horizon entropy, the non-equilibrium entropy production, and the entropy of all matter, field and energy components. We derive a universal condition to protect the generalized second law and study its validity in different gravity theories. In Einstein gravity, (even in the phantom-dominated universe with a Schwarzschild black hole), Lovelock gravity, and braneworld gravity, we show that the condition to keep the GSL can always be satisfied. In $f(R)$ gravity and scalar-tensor gravity, the condition to protect the GSL can also hold because the gravity is always attractive and the effective Newton constant should be approximate constant satisfying the experimental bounds.