Probabilistic Evolution of Black Hole Thermodynamic States via Fokker-Planck Equation

TL;DR

This paper models the probabilistic evolution of black hole thermodynamic states during phase transitions using the Fokker-Planck equation, revealing kinetic regimes and linking entropy production to barrier crossing.

Contribution

It introduces a stochastic framework for black hole phase transitions, connecting thermodynamic dissipation with the dynamics of the process.

Findings

Identifies two kinetic regimes in black hole phase transitions.

Shows phase transition correlates with a peak in entropy production.

Demonstrates barrier crossing driven by maximum thermodynamic dissipation.

Abstract

Employing the generalized free energy landscape and solving the associated Fokker-Planck equation, we obtain the time-dependent probability evolution of the order parameter for the RN-AdS black hole phase transitions. Our analysis reveals two distinct kinetic regimes, namely relaxation dynamics initialized at the unstable maximum and phase transition from the metastable state. Furthermore, we characterize the non-equilibrium irreversibility and macroscopic uncertainty using the entropy production rate and the Shannon entropy. The results demonstrate that the phase transition synchronizes exactly with a prominent peak in the entropy production rate, identifying the barrier crossing event as a process fundamentally driven by maximum thermodynamic dissipation.