  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.
