  It is well known that de Sitter(dS) black holes generally have a black hole
horizon and a cosmological horizon, both of which have Hawking radiation. But
the radiation temperature of the two horizons is generally different, so dS
black holes do not meet the requirements of thermal equilibrium stability,
which brings certain difficulties to the study of the thermodynamic
characteristics of black holes. In this paper, dS black hole is regarded as a
thermodynamic system, and the effective thermodynamic quantities of the system
are obtained. The influence of various state parameters on the effective
thermodynamic quantities in the massive gravity space-time is discussed. The
condition of the phase transition of the de Sitter black hole in massive
gravity space-time is given. We consider that the total entropy of the dS black
hole is the sum of the corresponding entropy of the two horizons plus an extra
term from the correlation of the two horizons. By comparing the entropic force
of interaction between black hole horizon and the cosmological horizon with
Lennard-Jones force between two particles, we find that the change rule of
entropic force between the two system is surprisingly the same. The research
will help us to explore the real reason of accelerating expansion of the
universe.
