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We study the first law of thermodynamics in IR modified Hv{o}rava-Lifshitz spacetime. Based on the Bekenstein-Hawking entropy, we obtain the integral formula and the differential formula of the first law of thermodynamics for the Kehagias-Sfetsos black hole by treating $omega$ as a new state parameter and redefining a mass that is just equal to $M_{ADM}$ obtained by Myungcite{YSM2} if we take $alpha=3pi/8$.
We extend to the Horndeski realm the irreversible thermodynamics description of gravity previously studied in first generation scalar-tensor theories. We identify a subclass of Horndeski theories as an out-of--equilibrium state, while general relativ
Using the solution phase space method, we investigate the thermodynamics of black holes in Einstein-aether-Maxwell theory, for which the traditional Wald method (covariant phase space method) fails. We show the first laws of thermodynamics and defini
A new generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is proposed without assuming symmetries, asymptotic flatness, or special spacetime metrics. The procedure followed is simple but powerful and consists of writing t
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({cal R})$ gravity as a non-equilibrium one. We apply Eckarts first order thermodynamics to the effective diss
Non-stationary null dust in a spherically symmetric spacetime is studied in the context of a general-covariant Horava-Lifshitz theory. The non-minimal coupling to matter is considered in the infrared limit. The aim of this paper is to study whether t