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The quantum Mpemba effects

Nature Reviews Physics volume 7, pages 451–460 (2025)Cite this article

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Abstract

The Mpemba effect, in which a hotter system can equilibrate faster than a cooler one, has long been a subject of fascination in classical physics. In the past few years, notable theoretical and experimental progress has been made in understanding its occurrence in both classical and quantum systems. In this Perspective, we provide a concise overview of recent work and open questions on the Mpemba effect in quantum systems, with a focus on both open and isolated dynamics, which give rise to distinct manifestations of this anomalous non-equilibrium phenomenon. We discuss key theoretical frameworks, highlight experimental observations and explore the fundamental mechanisms that give rise to anomalous relaxation behaviours. Particular attention is given to the role of quantum fluctuations, integrability and symmetry in shaping equilibration pathways.

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Fig. 1: Experimental observation of three quantum Mpemba effects.
Fig. 2: Reduced density matrix ρA and its symmetrization ρA,Q that enter in the definition of the entanglement asymmetry.
Fig. 3: Time evolution of the entanglement asymmetry in different systems.
Fig. 4: The quasiparticle picture for the entanglement asymmetry.

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Acknowledgements

The authors are deeply grateful to the many physicists who have collaborated with them over the past few years on the study of the quantum Mpemba effect. In particular, the authors thank V. Alba, B. Bertini, R. Blatt, F. Caceffo, K. Chalas, A. De Luca, F. Ferro, A. Foligno, J. Franke, L. Kh. Joshi, M. Joshi, I. Klich, K. Klobas, F. Kranzl, L. Piroli, A. Rath, C. Roos, C. Rylands, X. Turkeshi, B. Vermersch, E. Vernier, V. Vitale, S. Yamashika and P. Zoller. P.C. and F.A. acknowledge support from ERC under Consolidator Grant no. 771536 (NEMO) and from European Union — NextGenerationEU, in the framework of the PRIN Project HIGHEST no. 2022SJCKAH_002. S.M. acknowledges the support from the Walter Burke Institute for Theoretical Physics and the Institute for Quantum Information and Matter at Caltech.

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Authors and Affiliations

  1. SISSA and INFN, Trieste, Italy

    Filiberto Ares & Pasquale Calabrese

  2. International Centre for Theoretical Physics (ICTP), Trieste, Italy

    Pasquale Calabrese

  3. Walter Burke Institute for Theoretical Physics, Caltech, Pasadena, CA, USA

    Sara Murciano

  4. Department of Physics and IQIM, Caltech, Pasadena, CA, USA

    Sara Murciano

  5. Université Paris-Saclay, CNRS, LPTMS, Orsay, France

    Sara Murciano

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  1. Filiberto Ares
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Ares, F., Calabrese, P. & Murciano, S. The quantum Mpemba effects. Nat Rev Phys 7, 451–460 (2025). https://doi.org/10.1038/s42254-025-00838-0

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