Mpemba Effect in Many-Body Systems Near Equilibrium
Classical Physics
2026-03-17 v2 Disordered Systems and Neural Networks
Mesoscale and Nanoscale Physics
Optics
Abstract
The Mpemba effect, in which a system initially farther from equilibrium relaxes faster than a closer one, is often associated with nonlinear or far-from-equilibrium dynamics. We show that this effect can arise entirely within the linear-response regime of many-body systems. In reciprocal systems, a uniform Mpemba effect emerges for three or more degrees of freedom via spectral separation of fast and slow modes. Breaking reciprocity renders the relaxation operator non-normal, enabling a strict componentwise Mpemba effect, with the hotter state relaxing faster even in every individual degree of freedom.
Keywords
Cite
@article{arxiv.2603.11707,
title = {Mpemba Effect in Many-Body Systems Near Equilibrium},
author = {Philippe Ben-Abdallah},
journal= {arXiv preprint arXiv:2603.11707},
year = {2026}
}