  Utilizing the holographic dictionary from the proposal that treats Newton's
constant as a thermodynamic variable, we establish a thermodynamic topological
equivalence between the AdS black holes in the bulk and the thermal states in
the dual CFT. The findings further reveal that the thermodynamic topological
characteristics of the RegMax AdS black holes are strongly influenced by the
characteristic parameter of the regularized Maxwell theory. Additionally, we
investigate the phase transition between low and high entropy thermal states
within a canonical ensemble in the dual CFT. Our observations indicate that the
phase transition behavior of the thermal states mirrors that of the black
holes. By modeling the phase transition process as a stochastic process, we are
able to calculate the rates of phase transition between the thermal states.
This result enhances our understanding of the dominant processes involved in
the phase transition of the thermal states in the dual CFT.
