Probing black hole microstructure with the kinetic turnover of phase transition

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.