Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory |
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Authors: | Jie Jiang Xiongjun Fang Sijie Gao |
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Institution: | 1. Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China2. College of Education for the Future, Beijing Normal University, Zhuhai 519087, China3. Department of Physics, Beijing Normal University, Beijing 100875, China |
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Abstract: | Thermodynamics plays an important role in gravitational theories. It is a principle that is independent of gravitational dynamics, and there is still no rigorous proof to show that it is consistent with the dynamical principle. We consider a self-gravitating perfect fluid system with the general diffeomorphism-covariant purely gravitational theory. Based on the Noether charge method proposed by Iyer and Wald, considering static off/on-shell variational configurations, which satisfy the gravitational constraint equation, we rigorously prove that the extrema of the total entropy of a perfect fluid inside a compact region for a fixed total particle number demands that the static configuration is an on-shell solution after we introduce some appropriate boundary conditions, i.e., it also satisfies the spatial gravitational equations. This means that the entropy principle of the fluid stores the same information as the gravitational equation in a static configuration. Our proof is universal and holds for any diffeomorphism-covariant purely gravitational theories, such as Einstein gravity, \begin{document}$ f(R)$\end{document}![]() gravity, Lovelock gravity, f(Gauss-Bonnet) gravity and Einstein-Weyl gravity. Our result indicates the consistency between ordinary thermodynamics and gravitational dynamics. |
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Keywords: | entropy principle self-gravitating perfect fluid thermodynamics |
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