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.

中文翻译：

---

非最小耦合重力下的热力学第二定律

在目前的工作中，我们表明，如果物质和引力场非最小耦合，则热力学第二定律通常不成立。我们通过显式计算在充满尘埃和辐射的封闭的均质各向同性宇宙的情况下物质场的熵的演化来证明这一结果，表明在这种情况下，熵变的符号由演化决定宇宙 在这些修改的理论中保留热力学第二定律将需要对其进行概括以解决重力熵的贡献。