The Mpemba effect likes to hit a wall

TL;DR

This paper investigates the Mpemba effect, revealing that a hard boundary is crucial for its occurrence in polynomial potentials and highlighting the role of high-temperature initial states.

Contribution

It demonstrates that the Mpemba effect in polynomial potentials depends on boundary conditions and initial temperature regimes, extending previous understanding beyond double-well shapes.

Findings

The Mpemba effect requires a sufficiently hard boundary in polynomial potentials.

High-temperature initial states influence the manifestation of the Mpemba effect.

The effect is not limited to double-well potentials but can occur in simpler polynomial potentials.

Abstract

The historical Mpemba effect involves a first-order phase transition. This has prompted the experimental realization of microscopic proxies in the form of a colloidal particle trapped in an asymmetric double well, for which the Mpemba effect has indeed been observed. We establish that the existence of the one-dimensional Mpemba effect for a polynomial potential is driven solely by the presence of a hard enough boundary, irrespective of the potential's double-well shape. We then show that the physics of the underlying Mpemba effect is governed not only by single-well physics but also by the high-temperature initial regime.