Anomalous thermal relaxation of Langevin particles in a piecewise-constant potential

TL;DR

This paper investigates the thermal relaxation behavior of Langevin particles in a piecewise-constant potential, revealing the conditions under which the Mpemba effect occurs and its relation to metastable states, phase transitions, and topology.

Contribution

It uncovers the presence of the Mpemba effect without metastable states and links its occurrence to eigenvector changes and phase transitions, proposing topological methods for detection.

Findings

Mpemba effect exists without metastable states

Boundaries of effect regions relate to eigenvector changes or phase transitions

Topology can be used to identify the Mpemba effect in physical systems

Abstract

We consider the thermal relaxation of a particle in a piecewise-constant potential landscape subject to thermal fluctuations in the overdamped limit. We study the connection between the occurrence of the Mpemba effect, the presence of metastable states, and phase transitions as a function of the potential. We find that the Mpemba effect exists even in cases without metastable states. In the considered physical system, the borders of the areas where the effect happens correspond to either eigenvector changes of direction or to phase transitions. Finally, we discuss the topological aspects of the strong Mpemba effect and propose using topology to search for the Mpemba effect in a physical system.