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  • Letter
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Quantum Mpemba effect without global symmetries

Tanmay Bhore1, Lei Su2, Ivar Martin3,2, Aashish A. Clerk4, and Zlatko Papić1

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Phys. Rev. B 112, L121109 – Published 26 September, 2025

DOI: https://doi.org/10.1103/1td3-2vwf

Abstract

The Mpemba effect, where a system initially farther from equilibrium relaxes faster than one closer to equilibrium, has been extensively studied in classical systems and recently explored in quantum settings. While previous studies of the quantum Mpemba effect (QME) have largely focused on isolated systems with global symmetries, we argue that the QME is ubiquitous in generic, nonintegrable many-body systems lacking such symmetries, including U(1) charge conservation, spatial symmetries, and even energy conservation. Using paradigmatic models such as the quantum Ising model with transverse and longitudinal fields, we show that the QME can be understood through the energy density of initial states and their inverse participation ratio in the energy eigenbasis. Our findings provide a unified framework for the QME, linking it with classical thermal relaxation.

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References (77)

  1. E. B. Mpemba and D. G. Osborne, Cool? Phys. Educ. 4, 172 (1969).
  2. T. Keller, V. Torggler, S. B. Jäger, S. Schutz, H. Ritsch, and G. Morigi, Quenches across the self-organization transition in multimode cavities, New J. Phys. 20, 025004 (2018).
  3. M. Baity-Jesi, E. Calore, A. Cruz, L. A. Fernandez, J. M. Gil-Narvión, A. Gordillo-Guerrero, D. Iñiguez, A. Lasanta, A. Maiorano, E. Marinari et al., The Mpemba effect in spin glasses is a persistent memory effect, Proc. Natl. Acad. Sci. USA 116, 15350 (2019).
  4. A. Kumar and J. Bechhoefer, Exponentially faster cooling in a colloidal system, Nature (London) 584, 64 (2020).
  5. F. J. Schwarzendahl and H. Löwen, Anomalous cooling and overcooling of active colloids, Phys. Rev. Lett. 129, 138002 (2022).
  6. I. G.-A. Pemartãn, E. Mompó, A. Lasanta, V. Martãn-Mayor, and J. Salas, Shortcuts of freely relaxing systems using equilibrium physical observables, Phys. Rev. Lett. 132, 117102 (2024).
  7. H. C. Burridge and P. F. Linden, Questioning the Mpemba effect: Hot water does not cool more quickly than cold, Sci. Rep. 6, 37665 (2016).
  8. I. Klich, O. Raz, O. Hirschberg, and M. Vucelja, Mpemba index and anomalous relaxation, Phys. Rev. X 9, 021060 (2019).
  9. J. Bechhoefer, A. Kumar, and R. Chétrite, A fresh understanding of the Mpemba effect, Nat. Rev. Phys. 3, 534 (2021).
  10. R. Holtzman and O. Raz, Landau theory for the Mpemba effect through phase transitions, Commun. Phys. 5, 280 (2022).
  11. G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja, Speedups in nonequilibrium thermal relaxation: Mpemba and related effects, arXiv:2502.01758.
  12. F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba effects, Nat. Rev. Phys. 7, 451 (2025).
  13. F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially accelerated approach to stationarity in Markovian open quantum systems through the Mpemba effect, Phys. Rev. Lett. 127, 060401 (2021).
  14. J. Zhang, G. Xia, C.-W. Wu, T. Chen, Q. Zhang, Y. Xie, W.-B. Su, W. Wu, C.-W. Qiu, P.-X. Chen et al., Observation of quantum strong Mpemba effect, Nat. Commun. 16, 301 (2025).
  15. S. Kochsiek, F. Carollo, and I. Lesanovsky, Accelerating the approach of dissipative quantum spin systems towards stationarity through global spin rotations, Phys. Rev. A 106, 012207 (2022).
  16. R. Bao and Z. Hou, Accelerating relaxation in Markovian open quantum systems through quantum reset processes, arXiv:2212.11170.
  17. F. Ivander, N. Anto-Sztrikacs, and D. Segal, Hyperacceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment, Phys. Rev. E 108, 014130 (2023).
  18. Y.-L. Zhou, X.-D. Yu, C.-W. Wu, X.-Q. Li, J. Zhang, W. Li, and P.-X. Chen, Accelerating relaxation through Liouvillian exceptional point, Phys. Rev. Res. 5, 043036 (2023).
  19. A. K. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba effect in a quantum dot with reservoirs, Phys. Rev. Lett. 131, 080402 (2023).
  20. A. K. Chatterjee, S. Takada, and H. Hayakawa, Multiple quantum Mpemba effect: Exceptional points and oscillations, Phys. Rev. A 110, 022213 (2024).
  21. X. Wang and J. Wang, Mpemba effects in nonequilibrium open quantum systems, Phys. Rev. Res. 6, 033330 (2024).
  22. D. Liu, J. Yuan, H. Ruan, Y. Xu, S. Luo, J. He, X. He, Y. Ma, and J. Wang, Speeding up quantum heat engines by the Mpemba effect, Phys. Rev. A 110, 042218 (2024).
  23. S. Longhi, Photonic Mpemba effect, Opt. Lett. 49, 5188 (2024).
  24. X. Wang, J. Su, and J. Wang, Mpemba meets quantum chaos: Anomalous relaxation and Mpemba crossings in dissipative Sachdev-Ye-Kitaev models, arXiv:2410.06669.
  25. J. Furtado and A. C. Santos, Strong quantum Mpemba effect with squeezed thermal reservoirs, Ann. Phys. 480, 170135 (2025).
  26. D. Qian, H. Wang, and J. Wang, Intrinsic quantum Mpemba effect in Markovian systems and quantum circuits, Phys. Rev. B 111, L220304 (2025).
  27. L. P. Bettmann and J. Goold, Information geometry approach to quantum stochastic thermodynamics, Phys. Rev. E 111, 014133 (2025).
  28. J. W. Dong, H. F. Mu, M. Qin, and H. T. Cui, Quantum Mpemba effect of localization in the dissipative mosaic model, Phys. Rev. A 111, 022215 (2025).
  29. A. Nava and R. Egger, Mpemba effects in open nonequilibrium quantum systems, Phys. Rev. Lett. 133, 136302 (2024).
  30. I. Medina, O. Culhane, F. C. Binder, G. T. Landi, and J. Goold, Anomalous discharging of quantum batteries: The ergotropic Mpemba effect, Phys. Rev. Lett. 134, 220402 (2025).
  31. F. Kheirandish, N. Cheraghpour, and A. Moradian, The Mpemba effect in quantum oscillating and two-level systems, Phys. Lett. A 559, 130915 (2025).
  32. J. Graf, J. Splettstoesser, and J. Monsel, Role of electron-electron interaction in the Mpemba effect in quantum dots, J. Phys.: Condens. Matter 37, 195302 (2025).
  33. K. Zatsarynna, A. Nava, R. Egger, and A. Zazunov, Green's function approach to Josephson dot dynamics and application to quantum Mpemba effects, Phys. Rev. B 111, 104506 (2025).
  34. D. J. Strachan, A. Purkayastha, and S. R. Clark, Non-Markovian quantum Mpemba effect, arXiv:2402.05756.
  35. Z.-M. Wang, S. L. Wu, M. S. Byrd, and L.-A. Wu, Going beyond quantum Markovianity and back to reality: An exact master equation study, arXiv:2411.17197.
  36. P. Westhoff, S. Paeckel, and M. Moroder, Fast and direct preparation of a genuine lattice BEC via the quantum Mpemba effect, arXiv:2504.05549.
  37. S. Aharony Shapira, Y. Shapira, J. Markov, G. Teza, N. Akerman, O. Raz, and R. Ozeri, Inverse Mpemba effect demonstrated on a single trapped ion qubit, Phys. Rev. Lett. 133, 010403 (2024).
  38. M. E. Edo and L.-A. Wu, Study on quantum thermalization from thermal initial states in a superconducting quantum computer, arXiv:2403.14630.
  39. J. M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43, 2046 (1991).
  40. M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50, 888 (1994).
  41. M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature (London) 452, 854 (2008).
  42. F. Ares, S. Murciano, and P. Calabrese, Entanglement asymmetry as a probe of symmetry breaking, Nat. Commun. 14, 2036 (2023).
  43. S. Murciano, F. Ares, I. Klich, and P. Calabrese, Entanglement asymmetry and quantum Mpemba effect in the XY spin chain, J. Stat. Mech. (2024) 013103.
  44. C. Rylands, E. Vernier, and P. Calabrese, Dynamical symmetry restoration in the Heisenberg spin chain, J. Stat. Mech. (2024) 123102.
  45. S. Yamashika, F. Ares, and P. Calabrese, Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems, Phys. Rev. B 110, 085126 (2024).
  46. S. Yamashika, P. Calabrese, and F. Ares, Quenching from superfluid to free bosons in two dimensions: Entanglement, symmetries, and quantum Mpemba effect, Phys. Rev. A 111, 043304 (2025).
  47. X. Turkeshi, P. Calabrese, and A. D. Luca, Quantum Mpemba effect in random circuits, Phys. Rev. Lett. 135, 040403 (2025).
  48. K. Klobas, C. Rylands, and B. Bertini, Translation symmetry restoration under random unitary dynamics, Phys. Rev. B 111, L140304 (2025).
  49. S. Liu, H.-K. Zhang, S. Yin, and S.-X. Zhang, Symmetry restoration and quantum Mpemba effect in symmetric random circuits, Phys. Rev. Lett. 133, 140405 (2024).
  50. H. Yu, Z.-X. Li, and S.-X. Zhang, Symmetry breaking dynamics in quantum many-body systems, arXiv:2501.13459.
  51. F. Ares, S. Murciano, P. Calabrese, and L. Piroli, Entanglement asymmetry dynamics in random quantum circuits, Phys. Rev. Res. 7, 033135 (2025).
  52. K. Klobas, Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54, J. Phys. A: Math. Theor. 57, 505001 (2024).
  53. A. Foligno, P. Calabrese, and B. Bertini, Nonequilibrium dynamics of charged dual-unitary circuits, PRX Quantum 6, 010324 (2025).
  54. S. Liu, H.-K. Zhang, S. Yin, S.-X. Zhang, and H. Yao, Quantum Mpemba effects in many-body localization systems, arXiv:2408.07750.
  55. L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese et al., Observing the quantum Mpemba effect in quantum simulations, Phys. Rev. Lett. 133, 010402 (2024).
  56. C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Murciano, and B. Bertini, Microscopic origin of the quantum Mpemba effect in integrable systems, Phys. Rev. Lett. 133, 010401 (2024).
  57. P. Calabrese and J. Cardy, Evolution of entanglement entropy in one-dimensional systems, J. Stat. Mech. (2005) P04010.
  58. H. Kim and D. A. Huse, Ballistic spreading of entanglement in a diffusive nonintegrable system, Phys. Rev. Lett. 111, 127205 (2013).
  59. See Supplemental Material at http://link.aps.org/supplemental/10.1103/1td3-2vwf for additional numerical results and study of other models.
  60. L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016).
  61. A. Russotto, F. Ares, and P. Calabrese, Symmetry breaking in chaotic many-body quantum systems at finite temperature, Phys. Rev. E 112, L032101 (2025).
  62. F. Ares, V. Vitale, and S. Murciano, Quantum Mpemba effect in free-fermionic mixed states, Phys. Rev. B 111, 104312 (2025).
  63. F. Caceffo, S. Murciano, and V. Alba, Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems, J. Stat. Mech. (2024) 063103.
  64. D. J. Thouless, Electrons in disordered systems and the theory of localization, Phys. Rep. 13, 93 (1974).
  65. V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007).
  66. T. Prosen, Time evolution of a quantum many-body system: Transition from integrability to ergodicity in the thermodynamic limit, Phys. Rev. Lett. 80, 1808 (1998).
  67. T. Prosen, Quantum invariants of motion in a generic many-body system, J. Phys. A: Math. Gen. 31, L645 (1998).
  68. B. Bertini, P. Kos, and T. Prosen, Entanglement spreading in a minimal model of maximal many-body quantum chaos, Phys. Rev. X 9, 021033 (2019).
  69. M. Bukov, L. D'Alessio, and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering, Adv. Phys. 64, 139 (2015).
  70. J. I. Cirac, D. Pérez-García, N. Schuch, and F. Verstraete, Matrix product states and projected entangled pair states: Concepts, symmetries, theorems, Rev. Mod. Phys. 93, 045003 (2021).
  71. W. W. Ho, S. Choi, H. Pichler, and M. D. Lukin, Periodic orbits, entanglement, and quantum many-body scars in constrained models: Matrix product state approach, Phys. Rev. Lett. 122, 040603 (2019).
  72. A. Daniel, A. Hallam, J.-Y. Desaules, A. Hudomal, G.-X. Su, J. C. Halimeh, and Z. Papić, Bridging quantum criticality via many-body scarring, Phys. Rev. B 107, 235108 (2023).
  73. G. Vidal, Classical simulation of infinite-size quantum lattice systems in one spatial dimension, Phys. Rev. Lett. 98, 070201 (2007).
  74. M. C. Bañuls, J. I. Cirac, and M. B. Hastings, Strong and weak thermalization of infinite nonintegrable quantum systems, Phys. Rev. Lett. 106, 050405 (2011).
  75. C.-J. Lin and O. I. Motrunich, Quasiparticle explanation of the weak-thermalization regime under quench in a nonintegrable quantum spin chain, Phys. Rev. A 95, 023621 (2017).
  76. J. Ren, iTEBD.jl, https://github.com/jayren3996/iTEBD.jl.
  77. Data repository this paper, https://doi.org/10.5518/1741.

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Phys. Rev. B 112, L121109– Published 26 September, 2025
  • Received 28 May 2025
  • Accepted 21 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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