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

Probing black hole microstructure with the kinetic turnover of phase transition