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

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.

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• Mpemba effect in a Langevin system: population statistics, metastability and other exact results
• Mpemba effect in anisotropically driven inelastic Maxwell gases
• Anomalous relaxation from a non-equilibrium steady state: An isothermal analog of the Mpemba effect
• Asymmetries of thermal processes in open quantum systems
• Mpemba effect in the relaxation of an active Brownian particle in a trap without metastable states
• Mpemba effect on non-equilibrium active Markov chains