Extending the Mpemba effect to the underdamped realm

Shahaf Aharony Shapira; Gene Chen; Marija Vucelja; Oren Raz

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arXiv · 2607.11797

Extending the Mpemba effect to the underdamped realm

Shahaf Aharony Shapira·Gene Chen·Marija Vucelja·Oren Raz

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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.

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Shahaf Aharony Shapira, Gene Chen, Marija Vucelja, Oren Raz. 2026-07-13. Extending the Mpemba effect to the underdamped realm. https://arxiv.org/abs/2607.11797

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