Extending the Mpemba effect to the underdamped realm
arXiv:2607.11797
The paper investigates whether the Mpemba effect—where a hotter system cools faster than a colder one—occurs in underdamped (inertial) regimes, showing it can persist for moderate damping and exploring conditions where it does or does not appear.
Abstract
The Mpemba effect is the counterintuitive phenomenon in which an initially hotter system cools faster than a colder, otherwise identical system. It has been experimentally demonstrated in various classical overdamped systems. Here, we explore the existence of the same effect in a regime where inertia cannot be neglected, namely, the underdamped regime. We consider the underdamped dynamics of a Brownian particle in a potential. We show perturbatively that, if the effect exists in the overdamped limit, it persists for sufficiently large but finite damping. In the ultra-weak-damping limit, we show that the effect cannot occur for smooth confining single-well potentials with canonical initial states, but can arise in more complex potentials. We demonstrate our results numerically using double-well potentials, the canonical setting for the Mpemba effect in the overdamped limit.
15 pages, 7 figures