Entropic force between two horizons of dilaton black holes with a power-Maxwell field

In this paper, we consider $(n+1)$-dimensional topological dilaton de Sitter black holes with power-Maxwell field as thermodynamic systems. The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon respectively are interrelated. So 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 corrected term which is produced by the association of the two horizons. We analyze the entropic force produced by the corrected term at given temperatures, which is affected by parameters and dimensions of the space-time. It is shown that the change of entropic force with the position ratio of two horizons in some region is similar to that of Lennard-Jones force with the position of particles. If the effect of entropic force is similar to that of Lennard-Jones force, and other forces are absent, the motion of the cosmological horizon relative to the black hole horizon would have an oscillating process. The entropic force between the two horizons is probably one of the participants to drive the evolution of universe.