Dynamic property of phase transition for non-linear charged anti-de Sitter black holes

Understanding the thermodynamic phase transition of black holes can provide deep insights into the fundamental properties of black hole gravity and help to establish quantum gravity. In this work, we investigate the phase transition and its dynamics for the charged EPYM AdS black hole. Through reconstructing Maxwell's equalarea law, we find there exists a high-/low-potential black hole (HPBH/LPBL) phase transition, not only the pure large/small black hole phase transition. The Gibbs free energy landscape (G(L)) is treated as a function of the black hole horizon, which is the order parameter of the phase transition due to thermal fluctuation. From the viewpoint of G(L), the stable HPBH/LPBL states correspond to two wells of G(L), which have the same depth. The unstable intermediate-potential black hole state corresponds to the local maximum of G(L). Then we focus on the probability evolution governed by the Fokker -Planck equation. Through solving the Fokker -Planck equation with different reflection/absorption boundary conditions and initial conditions, the dynamics of switching between the coexistent HPBH and LPBL phases is probed within the first passage time. Furthermore, the effect of temperature on the dynamic properties of the phase transition is also investigated.