### Abstract

We show that it is possible to obtain a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density f (R, φ{symbol}, X), where R is the Ricci scalar and X is the kinetic energy of a scalar field φ{symbol}. This comes from a suitable definition of an energy-momentum tensor of the "dark" component that respects to a local energy conservation in the Jordan frame. In this framework the horizon entropy S corresponding to equilibrium thermodynamics is equal to a quarter of the horizon area A in units of gravitational constant G, as in Einstein gravity. For a flat cosmological background with a decreasing Hubble parameter, S globally increases with time, as it happens for viable f (R) inflation and dark energy models. We also show that the equilibrium description in terms of the horizon entropy S is convenient because it takes into account the contribution of both the horizon entropy over(S, ̂) in non-equilibrium thermodynamics and an entropy production term.

Original language | English |
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Pages (from-to) | 101-109 |

Number of pages | 9 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 688 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2010 Apr 26 |

Externally published | Yes |

### Keywords

- Cosmology
- Dark energy
- Evaporation
- Modified theories of gravity
- Quantum aspects of black holes
- Thermodynamics

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*688*(1), 101-109. https://doi.org/10.1016/j.physletb.2010.03.070