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

TL;DR

This paper investigates the thermodynamics and stochastic kinetics of phase transitions in Reissner-Nordström AdS black holes, revealing how free energy landscape topography influences state switching times and fluctuations.

Contribution

It introduces a stochastic framework using the Fokker-Planck equation to analyze black hole phase transition kinetics based on free energy landscapes.

Findings

Black hole stability is linked to free energy landscape topography.

State switching probabilities are influenced by thermal fluctuations.

Mean first passage times depend on barrier heights and temperature.

Abstract

We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordstr\"{o}m anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the 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 switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.