Equivalence of modified gravity equation to the Clausius relation

Abstract

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).

6 pages, no figure, several statements clarified, references added

References in corpus (7)

• Thermodynamic route to Field equations in Lanczos-Lovelock Gravity
• Dark Energy and Gravity
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Dark Energy: Mystery of the Millennium
• F(R) gravity equation of state
• Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
• The equation of state for scalar-tensor gravity

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