A resource theoretical unification of Mpemba effects: classical and quantum

TL;DR

This paper unifies classical and quantum Mpemba effects using resource theories, revealing how initial states and symmetry considerations govern anomalous relaxation behaviors across different physical systems.

Contribution

It introduces a resource-theoretic framework that unifies classical and quantum Mpemba effects, linking thermalization dynamics with symmetry and athermality resources.

Findings

Thermal Mpemba effect arises from athermality resource theory.

Quantum symmetry-restoring Mpemba effect is explained via asymmetry resource theory.

The dynamics split into symmetry-respecting and symmetry-breaking components.

Abstract

The Mpemba effect originally referred to the observation that, under certain thermalizing dynamics, initially hotter samples can cool faster than colder ones. This effect has since been generalized to other anomalous relaxation behaviors even beyond classical domains, such as symmetry restoration in quantum systems. This work demonstrates that resource theories, widely employed in information theory, provide a unified organizing principle to frame Mpemba physics. We show how the conventional thermal Mpemba effect arises naturally from the resource theory of athermality, while its symmetry-restoring counterpart is fully captured by the resource theories of asymmetry. Leveraging the framework of modes of asymmetry, we demonstrate that the Mpemba effect due to symmetry restoration is governed by the initial overlap with the slowest symmetry-restoring mode -- mirroring the role of the slowest Liouvillian eigenmode in thermal Mpemba dynamics. Through this resource-theoretical formalism, we uncover the connection between these seemingly disparate effects and show that the dynamics of thermalization naturally splits into a symmetry-respecting and a symmetry-breaking term.