Mpemba Effect in Many-Body Systems Near Equilibrium

TL;DR

This paper demonstrates that the Mpemba effect, typically linked to nonlinear dynamics, can occur in linear-response many-body systems through spectral separation and non-normal operators, revealing new mechanisms for faster relaxation.

Contribution

It introduces the occurrence of the Mpemba effect within linear-response regimes and explains how reciprocity and non-normality influence the relaxation dynamics.

Findings

Mpemba effect can occur in linear-response many-body systems.

Spectral separation of modes induces the effect in reciprocal systems.

Breaking reciprocity enables a componentwise Mpemba effect in all degrees of freedom.

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.