# Second law of thermodynamics in nonminimally coupled gravity

## TL;DR

This paper investigates how the second law of thermodynamics is affected in nonminimally coupled gravity theories, showing it generally does not hold unless modified to include gravitational entropy contributions.

## Contribution

It demonstrates that the second law fails in nonminimally coupled gravity unless extended to incorporate gravitational entropy, with explicit entropy evolution calculations in cosmological models.

## Key findings

- Second law of thermodynamics does not generally hold in nonminimally coupled gravity.
- Entropy evolution depends on the universe's dynamics in these theories.
- A generalized second law including gravitational entropy may be necessary.

## Abstract

In the present work we show that the second law of thermodynamics does not generally hold if the matter and gravitational fields are nonminimally coupled. We demonstrate this result by explicitly computing the evolution of the entropy of the matter fields in the case of a closed homogeneous and isotropic universe filled with dust and radiation, showing that, in this case, the sign of the entropy variation is determined by the evolution of the universe. The preservation of the second law of thermodynamics in these modified theories would require its generalization to account for a gravitational entropy contribution.