Estrada, MilkoAros, Rodrigo2021-08-302021-08-302019-09European Physical Journal C Volume 79, Issue 101 October 2019 Article number 8101434-6044http://repositorio.unab.cl/xmlui/handle/ria/20045Indexación: Scopus.In this work it is shown that the thermodynamics of regular black holes with a cosmological horizon, which are solutions of Lovelock gravity, determines that they must evolve either into a state where the black hole and cosmological horizons have reached thermal equilibrium or into an extreme black hole geometry where the black hole and cosmological horizons have merged. This differs from the behavior of Schwarzschild de Sitter geometry which evolves into a de Sitter space, the ground state of the space of solutions. This occurs due to a phase transition of the heat capacity of the black hole horizon. To perform that analysis it is shown that at each horizon a local first law of thermodynamics can be obtained from the gravitational equations. © 2019, The Author(s).enBlack HolesDilatonSitterArtículoAtribución 4.0 Internacional (CC BY 4.0)10.1140/epjc/s10052-019-7316-0