Overcoming Barriers: Kramers' Escape Rate Analysis of Metastable Dynamics in First-Order Multi-Phase Transitions

TL;DR

This paper applies Kramers' escape rate analysis to black hole phase transitions with multiple critical points, demonstrating its validity and exploring transition pathways in complex multi-minima energy landscapes.

Contribution

It extends the kinetic analysis of phase transitions to multi-critical black hole systems, validating the use of Kramers' escape rate in complex energy landscapes.

Findings

Kramers' escape rate remains valid in multi-minima black hole systems.

Transitions can occur via sequential or direct pathways between minima.

The study provides insights into the energetic landscapes of black hole phase transitions.

Abstract

The expanding application of classical thermodynamic methods to black hole physics has yielded significant advances in characterizing phase transition behavior. Among these approaches, thermodynamic analysis -- particularly kinetic formulations like the Kramers' escape rate -- provides a robust framework for probing black hole phase transitions with minimal relativistic constraints. This study investigates the kinetics and dynamic evolution of first-order phase transitions in black holes exhibiting multiple critical points, employing a particle-based escape rate model. The distinct free energy landscapes inherent to multi-critical systems, which can simultaneously support multiple local minima under specific thermodynamic conditions (temperature and pressure) within a given reference frame, raise fundamental questions regarding transition pathways. We rigorously assess whether the Kramers' escape rate retains its predictive validity in these complex multi-minima systems, as established for conventional single-minimum configurations. Furthermore, we examine whether transitions proceed via a sequential, stepwise mechanism between adjacent minima, or if pathways exist that bypass intermediate states through direct descent to the global minimum. Our analysis of black holes undergoing multiphase transitions reveals both parallels and significant deviations from single-transition models. Crucially, we demonstrate that the Kramers' escape rate remains a quantitatively reliable indicator of first-order phase transitions in black holes, even within multi-critical frameworks. This approach offers deeper insights into the governing energetic landscapes and kinetic processes underlying these phenomena.