Abstract In this paper we demonstrate that Boltzmann's H-theorem does not necessarily hold in the context of theories of gravity with nonminimally coupled matter fields. We find sufficient conditions for the violation of Boltzmann's H-theorem and derive an expression for the evolution of Boltzmann's H in terms of the nonminimal coupling function, valid in the case of a collisionless gas in a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker universe. We highlight the implications of this result for the evolution of the entropy of the matter fields, briefly discussing the role played by collisions between particles whenever they are relevant. We also suggest a possible link between the high entropy of the Universe and the weakness of gravity in the context of these theories.

中文翻译：

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玻尔兹曼 H 定理、熵和理论中的引力强度，在物质和几何之间具有非最小耦合

摘要 在本文中，我们证明了玻尔兹曼的 H 定理在具有非最小耦合物质场的引力理论的背景下不一定成立。我们找到了违反玻尔兹曼 H 定理的充分条件，并根据非最小耦合函数导出了玻尔兹曼 H 演化的表达式，这在均匀和各向同性的弗里德曼-勒梅特-罗伯逊-沃克中的无碰撞气体的情况下有效宇宙。我们强调了这一结果对物质场熵演化的影响，并简要讨论了粒子之间的碰撞在相关时所起的作用。在这些理论的背景下，我们还提出了宇宙的高熵与引力的弱点之间可能存在的联系。