  By treating black hole as the macroscopic stable state on the free energy
landscape, we propose that the stochastic dynamics of the black hole phase
transition can be effectively described by the Langevin equation or
equivalently by the Fokker-Planck equation in phase space. We demonstrate the
turnover of the kinetics for the charged anti-de Sitter black hole phase
transition, which shows that the mean first passage time is linear with the
friction in the high damping regime and inversely proportional to the friction
in the low damping regime. The fluctuations in the kinetics are shown to be
large/small in the high/low damping regime and the switching behavior from the
small fluctuations to the large fluctuations takes place at the kinetic
turnover point. Because the friction is a reflection of the microscopic degrees
of freedom acting on the order parameter of the black hole, the turnover and
the corresponding fluctuations of the phase transition kinetics can be used to
probe the black hole microstructure.
