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We explore the thermodynamics and the underlying kinetics of the van derWaals type phase transition of Reissner-Nordstr\"{o}m anti-de Sitter (RNAdS)black holes based on the free energy landscape. We show that the thermodynamicstabilities of the three branches of the RNAdS black holes are determined bythe underlying free energy landscape topography. We suggest that the large(small) RNAdS black hole can have the probability to switch to the small(large) black hole due to the thermal fluctuation. Such a state switchingprocess under the thermal fluctuation is taken as a stochastic process and theassociated kinetics can be described by the probabilistic Fokker-Planckequation. We obtained the time dependent solutions for the probabilisticevolution by numerically solving Fokker-Planck equation with the reflectingboundary conditions. We also investigated the first passage process whichdescribes how fast a system undergoes a stochastic process for the first time.The distributions of the first passage time switching from small (large) tolarge (small) black hole and the corresponding mean first passage time as wellas its fluctuations at different temperatures are studied in detail. Weconclude that the mean first passage time and its fluctuations are related tothe free energy landscape topography through barrier heights and temperatures.

Thermal Dynamic Phase Transition of Reissner-Nordstr\"{o}m Anti-de Sitter Black Holes on Free Energy Landscape