  Phase transition is a core content of black hole thermodynamics. This study
adopted the Kramer's escape rate method for describing the Brownian motion of
particles in an external field to investigate the intensity of the phase
transition between small and large black hole states. Some existing studies
mostly focused on the formal analysis of the thermodynamic phase transition of
black holes, but they neglected the detailed description of the phase
transition process. Our results show that the phase transition between small
and large black holes for charged anti-de Sitter (AdS) black holes presents
serious asymmetric features, and the overall process is dominated by the
transition from a small black hole to a large black hole. This study filled a
research gap of a stochastic process analysis on the issue of the first-order
phase transition rate in the AdS black hole.
