The Mpemba effect likes to hit a wall
arXiv:2604.01543
The paper investigates the Mpemba effect for a one‑dimensional overdamped particle in an asymmetric polynomial double‑well potential and shows that the presence of a hard wall, not the shape of the potential, is essential for the effect, which is explained by the fine structure of the initial distribution probing the potential tails.
Abstract
The original Mpemba effect refers to the idea that a macroscopic hot system cools faster than an initially colder one. In its microscopic and classical versions, the system is modeled as an overdamped particle in an external potential, and the corresponding Mpemba effect has been observed experimentally and explored theoretically. We establish that the existence of the one-dimensional Mpemba effect for a particle in an asymmetric polynomial double-well potential is driven solely by the presence of a hard wall, irrespective of the potential's double-well shape and metastability. The Mpemba effect disappears if we consider an infinitely large system. We then show that the underlying mechanism of the Mpemba effect is governed by the fine structure of the initial statistical population as it probes the tails of the potential, which also explains the Mpemba effect in single-well and symmetric double-well potentials.