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Equivalence of modified gravity equation to the Clausius relation · Around

2009

Equivalence of modified gravity equation to the Clausius relation

Bamba, Kazuharu, Geng, Chao-Qiang, Nojiri, Shin'ichi et al.

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We explicitly show that the equations of motion for modified gravity theories of $F(R)$-gravity, the scalar-Gauss-Bonnet gravity, $F(\mathcal{G})$-gravity and the non-local gravity are equivalent to the Clausius relation in thermodynamics.

In addition, we discuss the relation between the expression of the entropy and the contribution from the modified gravity as well as the matter to the definition of the energy flux (heat).

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T. Padmanabhan, arXiv:0903.1254 [hep-th]

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K. Bamba, C. Q. Geng and S. Tsujikawa, arXiv:0909.2159 [gr-qc]

Cited in the paper.