Entropic force between two horizons of dilaton black holes with a power-Maxwell field * *Supported by the National Natural Science Foundation of China (11705107, 11847123, 11475108, 11705106, 11605107), the Natural Science Foundation of Shanxi Province, China (201601D102004), the Scientific and Technological Innovation Programs of Higher Education Institutions of Shanxi Province, China (2019L0743, 2020L0471, 2020L0472)

Abstract

In this paper, we consider -dimensional topological dilaton de Sitter black holes with a power-Maxwell field as thermodynamic systems. The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon are interrelated. Therefore, the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a correction term which is produced by the association of the two horizons. We analyze the entropic force produced by the correction term at given temperatures, which is affected by the parameters and dimensions of the space-time. It is shown that the change of entropic force with the position ratio of the two horizons in some regions is similar to that of the variation of the Lennard-Jones force with the position of particles. If the effect of entropic force is similar to that of the Lennard-Jones force, and other forces are absent, the motion of the cosmological horizon relative to the black hole horizon should have an oscillating process. The entropic force between the two horizons is probably one of the participants in driving the evolution of the universe.