  For the higher-dimensional dS spacetime embedded with black holes with
non-linear charges, there are two horizons with different radiation
temperatures. By introducing the interplay between two horizons this system can
be regarded as an ordinary thermodynamic system in the thermodynamic
equilibrium described by the thermodynamic quantities
($T_{eff},~P_{eff},~V,~S,~\Phi_{eff}$). In this work, our focus is on the
thermodynamic properties of phase transition for the four-dimensional dS
spacetime with different values of the charge correction $\bar\phi$. We find
that with the increasing of the non-linear charge correction the two horizons
get closer and closer, and the correction entropy is negative which indicates
the interaction between the two horizons stronger and stronger. Furthermore,
the heat capacity at constant pressure, isobaric expansion coefficient, and the
isothermal compression coefficient have the schottky peak at the critical
point. However, the heat capacity as constant volume for the dS spacetime is
nonzero. Finally, the dynamical properties of phase transition for this system
have investigated based on Gibbs free energy, where exists the different
behavior with that for AdS black holes.
