  Since the black hole and cosmological horizons in the de Sitter (dS)
spacetime with the Reissner-Nordstrom (RN) black hole are not independent to
each other, which is caused by the gravitational effect, the interplay between
two horizons should be considered. Based on this, by introducing the
interactive entropy the RN-dS spacetime is analogous to a thermodynamic system
with various thermodynamic quantities, in which the thermodynamic laws still
hold on. In our work, the thermodynamic properties of the RN-dS spacetime are
mapped out in the induced phase space, which are similar to that in AdS black
holes. The phase transition of the RN-dS spacetime between the high-potential
and the low-potential black hole phases is observed. Compared with an ordinary
thermodynamic system, the similar behaviors about the Joule-Thomson expansion
and the critical exponents are also checked out. Finally, the scalar curvature
of two existent phases are presented to reveal the underlying microstructure
and nature of phase transition in the RN-dS spacetime, which opens a new window
to investigate the dS spacetime with black holes from a observational
perspective.
