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Resource-Theoretical Unification of Mpemba Effects: Classical and Quantum

Alessandro Summer1,2,*, Mattia Moroder1,2,†, Laetitia P. Bettmann1,‡, Xhek Turkeshi3,§, Iman Marvian4,5,∥, and John Goold1,2,¶

  • *Contact author: summera@tcd.ie
  • †Contact author: moroderm@tcd.ie
  • ‡Contact author: bettmanl@tcd.ie
  • §Contact author: turkeshi@thp.uni-koeln.de
  • ∥Contact author: iman.marvian@duke.edu
  • Contact author: gooldj@tcd.ie
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Phys. Rev. X 16, 011065 – Published 25 March, 2026

DOI: https://doi.org/10.1103/rbt4-psfd

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.

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Popular Summary

The Mpemba effect, where a hotter system cools faster than a warmer one, has puzzled scientists for centuries. We demonstrate that this counterintuitive phenomenon, along with its counterparts in symmetry restoration and quantum relaxation, can be unified under the framework of resource theories. By treating relaxation as the dissipation of a physical resource—such as athermality, asymmetry, or quantum coherence—we show that the effect occurs when a state with more initial resource overlaps less with the slowest relaxation mode of the dynamics. Our analysis reveals that the symmetry Mpemba effect, previously considered a quantum curiosity, can also manifest in purely classical Markovian systems. These results establish a general principle for predicting and engineering ultrafast relaxation across classical and quantum domains by controlling how resources are depleted.

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Phys. Rev. X 16, 011065– Published 25 March, 2026
  • Received 1 August 2025
  • Revised 20 November 2025
  • Accepted 6 January 2026
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