Second law of thermodynamics in nonminimally coupled gravity

¹ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP - Rua das Estrelas, PT4150-762 Porto, Portugal
² Centro de Astrofísica da Universidade do Porto - Rua das Estrelas, PT4150-762 Porto, Portugal
³ Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto - Rua do Campo Alegre 687, PT4169-007 Porto, Portugal
⁴ School of Physics and Astronomy, University of Birmingham - Birmingham, B15 2TT, UK

^(a) rplazevedo@fc.up.pt
^(b) pedro.avelino@astro.up.pt

Received: 17 April 2020
Accepted: 21 October 2020

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.