# Equilibrium thermodynamics in modified gravitational theories - General Relativity and Quantum Cosmology

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Abstract: We show that it is possible to obtain a picture of equilibrium thermodynamicson the apparent horizon in the expanding cosmological background for a wideclass of modified gravity theories with the Lagrangian density $fR, \phi, X$,where $R$ is the Ricci scalar and $X$ is the kinetic energy of a scalar field$\phi$. This comes from a suitable definition of an energy momentum tensor ofthe -dark- component that respects to a local energy conservation in the Jordanframe. In this framework the horizon entropy $S$ corresponding to equilibriumthermodynamics is equal to a quarter of the horizon area $A$ in units ofgravitational constant $G$, as in Einstein gravity. For a flat cosmologicalbackground with a decreasing Hubble parameter, $S$ globally increases withtime, as it happens for viable $fR$ inflation and dark energy models. We alsoshow that the equilibrium description in terms of the horizon entropy $S$ isconvenient because it takes into account the contribution of both the horizonentropy $\hat{S}$ in non-equilibrium thermodynamics and an entropy productionterm.

Author: ** Kazuharu Bamba, Chao-Qiang Geng, Shinji Tsujikawa**

Source: https://arxiv.org/