The Kramers escape rate of phase transitions for the 6-dimensional Gauss-Bonnet AdS black hole with triple phases

TL;DR

This paper investigates the phase transition dynamics of a 6-dimensional Gauss-Bonnet AdS black hole with three stable states, using free energy analysis and Kramers escape rate to understand transition processes and key temperatures.

Contribution

It introduces a detailed analysis of triple-phase transitions in higher-dimensional black holes using stochastic methods and generalized free energy.

Findings

Six possible phase transition processes identified.

Two key temperatures associated with phase transitions.

Dynamic equilibrium processes between black hole states.

Abstract

In this study, we obtain specific picture of the phase transitions for the 6-dimensional Gauss-Bonnet Anti-de Sitter (AdS) black hole with triple phases, using the generalized free energy we constructed and Kramers escape rate in stochastic motion. There are six possible phase transition processes between the three different stable states (small, medium, and large black hole states). During these phase transitions, there are two key temperatures. One is the temperature at which the medium black hole state emerges, and the other is the temperature at which the small black hole state annihilates. Meanwhile, two dynamic equilibrium processes are formed. One is a dynamic equilibrium of the transition from the medium black hole state to the large black hole state and the transition from the small black hole state to the medium black hole state. The other is a dynamic equilibrium of the transition from the small black hole state to the medium black hole state and the transition from the medium black hole state to the small black hole state.