Dynamical horizon entropy and equilibrium thermodynamics of generalized gravity theories

Abstract

We study the relation between the thermodynamics and field equations of generalized gravity theories on the dynamical trapping horizon with sphere symmetry. We assume the entropy of dynamical horizon as the Noether charge associated with the Kodama vector and point out that it satisfies the second law when a Gibbs equation holds. We generalize two kinds of Gibbs equations to Gauss-Bonnet gravity on any trapping horizon. Based on the quasi-local gravitational energy found recently for $f(R)$ gravity and scalar-tensor gravity in some special cases, we also build up the Gibbs equations, where the nonequilibrium entropy production, which is usually invoked to balance the energy conservation, is just absorbed into the modified Wald entropy in the FRW spacetime with slowly varying horizon. Moreover, the equilibrium thermodynamic identity remains valid for $f(R)$ gravity in a static spacetime. Our work provides an alternative treatment to reinterpret the nonequilibrium correction and supports the idea that the horizon thermodynamics is universal for generalized gravity theories.

23 pages, no figure, minor changes, accepted for publication in Phys. Rev. D

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• Thermodynamic Behavior of particular $f(R,T)$ Gravity Models
• The P-V Phase Transition of the FRW Universe
• Dynamical Black Holes in 2+1 Dimensions
• The Unified First law in "Cosmic Triad" Vector Field Scenario
• Eternal inflation and a thermodynamic treatment of Einstein's equations
• Quasilocal energy and thermodynamic equilibrium conditions
• Gravitational thermodynamics and universal holographic duality in dynamical spacetimes