  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.
