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The quantum Mpemba effects

T0 review · 3 major / 5 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read The paper argues that quantum Mpemba effects are real in both open and isolated systems and are less controversial than the classical water-cooling phenomenon.

desk verdict A useful, well-organized review of the quantum Mpemba literature; the 'less controversial' claim is slightly stronger than the evidence, but the paper gives readers the tools to judge that themselves. read the letter →

arxiv 2502.08087 v1 pith:AZYYNWTS submitted 2025-02-12 cond-mat.stat-mech quant-ph

Filiberto Ares , Pasquale Calabrese , Sara Murciano This is my paper · ORCID
classification cond-mat.stat-mechquant-ph
keywords quantumMpembaeffectentanglementasymmetryopensystemsquenchintegrabilitysymmetryrestorationLindbladdynamicsnon-equilibriumrelaxation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review argues that the quantum Mpemba effect is real: a system that starts farther from equilibrium can relax faster than one that starts closer, in both open and isolated quantum systems. In open systems, relaxation is governed by the decay of the slowest mode of the dissipative dynamics, and a specially chosen initial state can suppress that mode, producing exponentially fast relaxation. In isolated systems, the effect is seen as symmetry restoration: an initial state that breaks a conservation-law symmetry more strongly can restore it sooner, with the entanglement asymmetry providing the quantitative measure. The review's conclusion is that trapped-ion experiments and quantum simulators have already observed these effects, making the quantum versions less contested than the classical phenomenon.

What carries the argument

The entanglement asymmetry, $\Delta S_A^{(n)} = S^{(n)}(\rho_{A,Q}) - S^{(n)}(\rho_A)$, compares a subsystem's reduced density matrix with its charge-symmetrized version and vanishes exactly when the symmetry is restored; it is the main probe for the isolated-system effect. For open systems, the machinery is the Lindblad spectrum: the slowest-decaying eigenmode controls relaxation, and a unitary rotation of the initial state can zero out its weight to produce the strong Mpemba effect. For integrable quenches, the quasiparticle picture carries the argument: entangled pairs emitted at each point propagate at model-dependent velocities, and each pair contributes to symmetry breaking only while both excitations remain inside the subsystem, so state-dependent pair velocities decide which initial state restores symmetry first.

What would settle it

Run the 12-ion quench with the unitary Hamiltonian only, measuring the Rényi-2 entanglement asymmetry for several tilting angles; if the asymmetry curves for differently tilted initial states never cross, the isolated-system quantum Mpemba effect as described in the review is falsified.

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Extended reading notes

Core claim

The paper's central claim is that the quantum Mpemba effect is a genuine, well-characterized family of phenomena with two complementary manifestations. In open Markovian systems, the approach to the steady state is controlled by the slowest-decaying eigenmode of the dissipative generator, and a unitary rotation of the initial state can completely suppress this mode, yielding the strong Mpemba effect of exponentially faster relaxation; reversing the setting gives the inverse effect, where a colder state heats faster. In isolated systems after a quantum quench, the relevant relaxation is the local restoration of a symmetry broken by the initial state, and a crossing of entanglement-asymmetry curves means that the more broken symmetry is restored faster. For integrable chains, the review adopts the quasiparticle explanation: entangled pairs propagate ballistically, and the more asymmetric initial state wins when the quasiparticles carrying most symmetry-breaking correlations are the fastest.

Load-bearing premise

The review's central narrative depends on the cited trapped-ion experiments and on the theoretical rule that faster ballistic pairs of entangled excitations explain symmetry restoration in exactly solvable chains; if either is wrong, the claimed convergence of evidence would be significantly weakened.

Editorial extensions

If this is right

  • If the review is right, the classical controversy about whether the Mpemba effect is genuinely physical is less pressing in quantum settings, because the effect can be defined and probed through state distances and symmetry restoration.
  • In integrable one-dimensional systems, the effect is determined only by the density of occupied quasiparticle modes and their velocities, giving a criterion that can be checked within each exactly solvable model.
  • The strong and inverse effects in open systems imply that controlled initial-state engineering, not just temperature, can exponentially accelerate or reverse thermal relaxation.
  • The trapped-ion demonstrations imply that the effect survives realistic imperfections such as dephasing, decoherence, interactions, and weak disorder.
  • A practical consequence is a non-adiabatic route to preparing thermal states, which the review identifies as promising for quantum simulation and control.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The review does not spell out that the entanglement-asymmetry crossing could be repurposed as a practical diagnostic on noisy intermediate-scale quantum devices, since it requires only randomized measurements and classical post-processing.
  • The authors leave implicit a design principle for open systems: aim for initial states orthogonal to the slowest relaxation mode, turning the strong Mpemba effect into a constructive target for state preparation.
  • A natural testable extension is whether the quasiparticle velocity criterion survives weak integrability breaking; the criterion gives a precise starting point for numerics on perturbed integrable chains.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This review surveys the quantum Mpemba effect in two settings: open Markovian quantum systems, where relaxation is driven by classical-like fluctuations, and isolated unitary systems, where relaxation is driven by quantum fluctuations. It introduces several distance measures used to detect the effect (trace distance, Frobenius distance, relative entropy, order parameters, and entanglement asymmetry), summarizes recent experiments on trapped ions and single qubits, reviews the quasiparticle mechanism for integrable systems, and discusses random-circuit and many-body-localized results. The central claim, stated in the abstract and introduction, is that quantum manifestations of the Mpemba effect are less controversial than classical ones and provide a clearer and more rigorous framework for understanding the phenomenon.

Significance. If the cited body of work is reliable, this is a timely and useful review of a rapidly expanding literature, written by three central contributors to the subject. Its strengths include a clear organization around open versus isolated dynamics, a concise presentation of the main theoretical tools, and a reasonably complete coverage of recent experimental confirmations, including the trapped-ion experiments of Refs. 43, 47, and 76. The review also explicitly flags some subtleties, such as the multiple crossings reported in Ref. 84. As a review, it contains no new derivations and no machine-checkable code; its value rests on the accuracy of roughly one hundred external references, which cannot be independently verified in this report. The comparative claim that quantum Mpemba effects are 'less controversial' is the part of the manuscript that most needs additional critical scrutiny.

major comments (3)
  1. [Introduction and Box 1] The abstract and introduction claim that quantum manifestations of the Mpemba effect are 'less controversial' and provide a 'clearer and more rigorous framework,' but the review never addresses whether the effect is independent of the chosen distance measure. Box 1 lists several inequivalent probes, and the text itself notes that the Frobenius distance is not monotonic under Markovian dynamics and that the entanglement asymmetry measures only symmetry restoration, not distance to the stationary state. As a result, two initial states could exhibit a Mpemba crossing for one probe but not for another, which would undermine the claimed rigor. I recommend adding a dedicated discussion of probe dependence, including the dependence on Rényi index and subsystem size when the entanglement asymmetry is used, and using the trapped-ion experiment of Ref. 76, where both the asymmetry and the Frobenius distance showed the same qualitative behavior, as a positive but limited example.
  2. [Quantifying the distance from equilibrium and 'Further results in integrable systems'] The operational definition of the Mpemba effect near the end of the 'Quantifying the distance from equilibrium' section requires a crossing time t_M after which the inequality d(ρ1(t)) < d(ρ2(t)) holds for all t > t_M. However, the later discussion of Ref. 84 states that tight-binding asymmetries can exhibit multiple crossings and that 'the existence of the quantum Mpemba effect cannot be inferred from the dynamics of the system at short times.' These two statements are not reconciled: a crossing that is later spoiled by a second crossing would satisfy the initial 'crossing' signature but not the persistent definition. The review should clarify whether the definition is meant to require persistent ordering and how the multiple-crossing phenomenon of Ref. 84 fits within the claimed rigorous framework.
  3. [Outlook] The outlook states that the quantum Mpemba effect 'offers an alternative, non-adiabatic pathway for preparing desired thermal states.' This is presented as a promising application, but no quantitative argument or reference is given for why the effect can be exploited for state preparation without additional overhead. I suggest marking this as a speculative direction and citing any existing work on protocol design or complexity, or softening the claim.
minor comments (5)
  1. [Author affiliations] The affiliation for SISSA reads 'T rieste'; it should be 'Trieste'.
  2. [References] Reference 22 is missing a period after 'effect'; it reads 'A fresh understanding of the Mpemba effectNature Rev. Phys.'.
  3. [Figure 4] The caption of Fig. 4 does not explain the parameters γ and h shown in panel (a) or identify which curve corresponds to which initial state; a legend or a sentence in the caption would improve readability.
  4. [Throughout] The text uses 'Schrodinger' without the umlaut; standardize to 'Schrödinger'.
  5. [Reference list] Many entries are arXiv preprints that may have since appeared in journals; updating them would increase the usefulness of the review for readers.
Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The review introduces no new free parameters or invented entities. It relies on the standard assumptions of the field, including Lindblad dynamics for open systems, the entanglement asymmetry as a probe of symmetry breaking, and the quasiparticle picture for integrable quenches. Its conclusions also assume the reliability of the cited experiments.

assumptions (4)
  • domain assumption Lindblad master equation correctly describes open quantum system dynamics
    Used throughout the open-systems section (e.g., Refs 41-43,45).
  • domain assumption The entanglement asymmetry is a faithful measure of symmetry breaking and relaxation
    Central probe in the isolated-systems section (Refs 33,76,77).
  • domain assumption The quasiparticle picture accurately describes symmetry restoration in integrable quenches
    Invoked in the 'Microscopic origin in integrable systems' section (Ref 77).
  • domain assumption The cited experimental results are reliable
    The review's conclusions about existence of the effect depend on experiments in Refs 43,47,76.

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Cite this review

Pith. "Pith review of The quantum Mpemba effects." pith.science (2026). https://pith.science/paper/AZYYNWTS

@misc{pith2026250208087,
  author       = {Pith},
  title        = {Pith review of: The quantum Mpemba effects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AZYYNWTS}},
  note         = {Machine review of arXiv:2502.08087}
}
read the original abstract

The Mpemba effect, where 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, significant theoretical and experimental progress has been made in understanding its occurrence in both classical and quantum systems. In this review, we provide a concise overview of 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 behaviors. Particular attention is given to the role of quantum fluctuations, integrability, and symmetry in shaping equilibration pathways. Finally, we outline open questions and future directions.

Figures

Figures reproduced from arXiv: 2502.08087 by the authors.

Figure 2
Figure 2. Reduced density matrix ρA and its symmetrization ρA,Q that enter in the definition of the entanglement asymmetry33. We consider a U(1) symmetry generated by a charge Q that decomposes into the contributions of the subsystems A and A¯, Q = QA +QA¯. If ρA is not symmetric, i.e. [ρA,QA] ̸= 0, then it is not block-diagonal in the eigenbasis of QA. By projecting over the eigenspaces of QA, we get the block-diagonal densi… view at source ↗
Figure 3
Figure 3. Sketch of the quasiparticle picture for the entanglement asymmetry. The quantum quench of a one￾dimensional integrable system generates pairs of entangled quasiparticles that propagate ballistically with opposite momentum. Each pair contributes to the charged moment Zn(α), from which the entanglement asymmetry can be calculated using Eq. (1). When specializing to the quotient Zn(α)/Zn(0), only the pairs with both ex… view at source ↗
Figure 4
Figure 4. Time evolution of the entanglement asymmetry in different systems. Panel a corresponds to Ref. 81, where the dynamics of the asymmetry is studied in a subsystem of ℓ = 100 sites of an infinite fermionic tight-binding chain from different initial states parameterized by h and γ. Panel b (c) shows the results obtained in Ref. 92 for the asymmetry of a tilted (anti)ferromagnetic state (with tilting angle θ) that evolve… view at source ↗

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Forward citations

Cited by 10 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement asymmetry in the gapped XYZ spin-$\frac12$ chain

    cond-mat.stat-mech 2026-07 conditional novelty 8.0 of 10

    In the gapped XYZ chain, the Rényi entanglement asymmetry of a large interval is ½ log(πℓχzz) + log n/(2(n−1)), with χzz/M computed from sine-Gordon form factors.

  2. Boundary quenches in (1+1)-dimensional conformal field theory

    cond-mat.stat-mech 2026-07 accept novelty 7.0 of 10

    A boundary quench in a (1+1)-d CFT makes one-point functions switch from old to new ground state across a light cone and makes adjacent-region entanglement jump by log(g_b/g_a).

  3. Prethermal inverse Mpemba effect

    cond-mat.stat-mech 2025-07 conditional novelty 7.0 of 10

    A colder initial state reaches a higher-energy prethermal plateau faster than a hotter state in a driven isolated quantum system, a new prethermal inverse Mpemba effect.

  4. Entanglement Asymmetry in Random Quantum Automata

    cond-mat.stat-mech 2026-07 accept novelty 6.0 of 10

    In random quantum automaton ensembles, the subsystem symmetrization scale depends on the initial state's participation entropy, and the onset of U(1) entanglement asymmetry coincides with the onset of subsystem coherence.

  5. (A)Symmetric Complexity and the Quantum Mpemba Effect

    hep-th 2025-09 conditional novelty 6.0 of 10

    A new decomposition of Krylov complexity into projected symmetric and asymmetric parts diagnoses the quantum Mpemba effect, but its claimed t=0 predictor is computationally equivalent to time evolution.

  6. Green's Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects

    cond-mat.mes-hall 2025-01 conditional novelty 6.0 of 10

    A Green's function approach predicts both types of quantum Mpemba effect in phase-quenched Josephson dots, including spin-orbit and Zeeman-coupled junctions.

  7. Quantum Mpemba effect in holography

    hep-th 2026-07 conditional novelty 5.0 of 10

    In a holographic superfluid, quenching from stronger symmetry breaking relaxes faster to equilibrium, with the slowest decay mode suppressed and the second mode amplified.

  8. Hilbert subspace imprint: a new mechanism for non-thermalization

    quant-ph 2025-06 conditional novelty 5.0 of 10

    Weak symmetry breaking or shallow-circuit state engineering can confine a quantum state to a polynomially small set of eigenstates, yielding non-thermal dynamics the authors call Hilbert subspace imprint.

  9. The Mpemba effect in quantum oscillating and two-level systems

    quant-ph 2024-12 conditional novelty 4.0 of 10

    Trace-distance crossings identified as quantum Mpemba effect are shown for a harmonic oscillator and a two-level system with time-dependent coupling to a single bath mode.

  10. Quantum Mpemba Effects from Symmetry Perspectives

    quant-ph 2025-07 conditional novelty 3.0 of 10

    A review arguing that the quantum Mpemba effect in closed systems is driven by unequal thermalization rates of different symmetry sectors, with entanglement asymmetry and charge variance playing complementary roles.

Reference graph

Works this paper leans on

105 extracted references · 46 canonical work pages · cited by 10 Pith papers

  1. [1]

    E. B. Mpemba and D. G. Osborne,Cool? Phys. Educ.4, 172 (1969)

    1969

  2. [2]

    Aristotle, Meterologica, Clarendon Press, Oxford (1923). 9/14

    1923

  3. [3]

    Bacon,Opus Majus, Russell and Russell, New York (1962)

    R. Bacon,Opus Majus, Russell and Russell, New York (1962)

    1962

  4. [4]

    Bacon,Novum Organum Scientiarum, Cambridge University Press, Cambridge (1620)

    F. Bacon,Novum Organum Scientiarum, Cambridge University Press, Cambridge (1620)

  5. [5]

    Descartes,Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences, Hackett, New York (1937)

    R. Descartes,Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences, Hackett, New York (1937)

    1937

  6. [6]

    L. R. Groves,Now It Can Be Told: The Story of the Manhattan Project, Harper & Row, New York (1962)

    1962

  7. [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)

    2016

  8. [8]

    H. C. Burridge and O. Hallstadius,Observing the Mpemba effect with minimal bias and the value of the Mpemba effect to scientific outreach and engagement, Proc. R. Soc. A476, 20190829 (2020)

    2020

Show all 105 references
  1. [9]

    Greaney, G

    A. Greaney, G. Lani, G. Cicero, and J. C. Grossman,Mpemba-like behavior in carbon nanotube resonators, Metall. Mater. Trans. A42, 3907 (2011)

    2011

  2. [10]

    Y. H. Ahn, H. Kang, D. Y. Koh, and H. Lee,Experimental verifications of Mpemba-like behaviors of clathrate hydrates, Korean J. Chem. Eng.33, 1903 (2016)

    2016

  3. [11]

    Lasanta, F

    A. Lasanta, F. Vega Reyes, A. Prados, and A. Santos,When the hotter cools more quickly: Mpemba effect in granular fluids, Phys. Rev. Lett.119, 148001 (2017)

    2017

  4. [12]

    C. Hu, J. Li, S. Huang, H. Li, C. Luo, J. Chen, S. Jiang, and L. An,Conformation directed mpemba effect on polylactide crystallization, Crystal Growth & Design18, 5757 (2018)

    2018

  5. [13]

    Keller, V

    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)

    2018

  6. [14]

    Baity-Jesi, E

    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, V. Martin-Mayor, J. Moreno-Gordo, A. Muñoz-Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, S. ...

    2019

  7. [15]

    F. J. Schwarzendahl and H. Löwen,Anomalous cooling and overcooling of active colloids, Phys. Rev. Lett. 129, 138002 (2022)

    2022

  8. [16]

    Holtzman and O

    R. Holtzman and O. Raz,Landau theory for the Mpemba effect through phase transitions, Comm. Phys.5, 280 (2022)

    2022

  9. [17]

    G. Teza, R. Yaacoby, and O. Raz,Relaxation shortcuts through boundary coupling, Phys. Rev. Lett.131, 017101 (2023)

    2023

  10. [18]

    González-Adalid Pemartín, E

    I. González-Adalid Pemartín, E. Mompó, A. Lasanta, V. Martín-Mayor, and J. Salas,Shortcuts of freely relaxing systems using equilibrium physical observables, Phys. Rev. Lett.132, 117102 (2024)

    2024

  11. [19]

    Lu and O

    Z. Lu and O. Raz,Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse, PNAS 114, 5083 (2017)

    2017

  12. [20]

    Klich, O

    I. Klich, O. Raz, O. Hirschberg, and M. Vucelja,Mpemba Index and Anomalous Relaxation, Phys. Rev. X9, 021060 (2019)

    2019

  13. [21]

    Kumar and J

    A. Kumar and J. Bechhoefer,Exponentially faster cooling in a colloidal system, Nature584, 64 (2020)

    2020

  14. [22]

    Bechhoefer, A

    J. Bechhoefer, A. Kumar, and R. Chétrite,A fresh understanding of the Mpemba effectNature Rev. Phys.3, 534 (2021)

    2021

  15. [23]

    Gal and O

    A. Gal and O. Raz,Precooling strategy allows exponentially faster heating, Phys. Rev. Lett.124, 060602 (2020)

    2020

  16. [24]

    Kumar, R

    A. Kumar, R. Chétrite, and J. Bechhoefer,Anomalous heating in a colloidal system, PNAS119, e2118484119 (2022)

    2022

  17. [25]

    M. R. Walker and M. Vucelja,Mpemba effect in terms of mean first passage times of overdamped Langevin dynamics on a double-well potential, arXiv:2212.07496

    arXiv

  18. [26]

    M. R. Walker, S. Bera, and M. Vucelja, Optimal transport and anomalous thermal relaxations , arXiv:2307.16103. 10/14

    arXiv

  19. [27]

    S. Bera, M. R. Walker, and M. Vucelja,Effect of dynamics on anomalous thermal relaxations and information exchange, arXiv:2308.04557

    arXiv

  20. [28]

    Santos,Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law, Phys

    A. Santos,Mpemba meets Newton: Exploring the Mpemba and Kovacs effects in the time-delayed cooling law, Phys. Rev. E109, 044149 (2024)

    2024

  21. [29]

    Van Vu and H

    T. Van Vu and H. Hayakawa,Thermomajorization Mpemba Effect, arXiv:2410.06686

    arXiv

  22. [30]

    G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja,Speedups in nonequilibrium thermal relaxation: Mpemba and related effects, arXiv:2502.01758

  23. [31]

    Wang and S

    X. Wang and S. G. Schirmer,Contractivity of the Hilbert-Schmidt distance under open-system dynamics, Phys. Rev. A79, 052326 (2009)

    2009

  24. [32]

    Moroder, O

    M. Moroder, O. Culhane, K. Zawadzki and J. Goold,Thermodynamics of the quantum Mpemba effect, Phys. Rev. Lett.133, 140404 (2024)

    2024

  25. [33]

    F. Ares, S. Murciano, and P. Calabrese,Entanglement asymmetry as a probe of symmetry breaking, Nature Comms. 14, 2036 (2023)

    2023

  26. [34]

    J. A. Vaccaro, F. Anselmi, H. M. Wiseman, and K. Jacobs,Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules, Phys. Rev. A77, 032114 (2008)

    2008

  27. [35]

    G. Gour, I. Marvian, and R. W. Spekkens,Measuring the quality of a quantum reference frame: The relative entropy of frameness, Phys. Rev. A80, 012307 (2009)

    2009

  28. [36]

    Chitambar and G

    E. Chitambar and G. Gour,Quantum resource theories, Rev. Mod. Phys.91, 025001 (2019)

    2019

  29. [37]

    Casini, M

    H. Casini, M. Huerta, J. M. Magán, and D. Pontello,Entanglement entropy and super-selection sectors. Part I. Global symmetries, JHEP02 (2020) 014

    2020

  30. [38]

    Casini, M

    H. Casini, M. Huerta, J. M. Magán, and D. Pontello,Entropic order parameters for the phases of QFT, JHEP 04 (2021) 277

    2021

  31. [39]

    Auerbach,Supercooling and the Mpemba effect: When hot water freezes quicker than cold, Am

    D. Auerbach,Supercooling and the Mpemba effect: When hot water freezes quicker than cold, Am. J. Phys. 63, 882 (1995)

    1995

  32. [40]

    Esposito, R

    S. Esposito, R. De Risi, and L. Somma,Mpemba effect and phase transitions in the adiabatic cooling of water before freezing, Physica A387, 757 (2008)

    2008

  33. [41]

    Nava and M

    A. Nava and M. Fabrizio,Lindblad dissipative dynamics in the presence of phase coexistence, Phys. Rev. B 100, 125102 (2019)

    2019

  34. [42]

    Carollo, A

    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)

    2021

  35. [43]

    Zhang, G

    J. Zhang, G. Xia, C.-W. Wu, T. Chen, Q. Zhang, Y. Xie, W.-B. Su, W. Wu, C.-W Qiu, P. Chen, W. Li, H. Jing. Y.-L. Zhou,Observation of quantum strong Mpemba effect, Nature Comms.16, 301 (2025)

    2025

  36. [44]

    L. P. Bettmann and J. Goold,Information geometry approach to quantum stochastic thermodynamics, Phys. Rev. E111, 014133 (2025)

    2025

  37. [45]

    A. K. Chatterjee, S. Takada and H. Hayakawa,Quantum Mpemba effect in a quantum dot with reservoirs, Phys. Rev. Lett.131, 080402 (2023)

    2023

  38. [46]

    A. K. Chatterjee, S. Takada and H. Hayakawa,Multiple quantum Mpemba effect: exceptional points and oscillations, Phys. Rev. A110, 022213 (2024)

    2024

  39. [47]

    S. A. 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)

    2024

  40. [48]

    Manikandan,Equidistant quenches in few-level quantum systems, Phys

    S.K. Manikandan,Equidistant quenches in few-level quantum systems, Phys. Rev. Res.3, 043108 (2021)

    2021

  41. [49]

    Kochsiek, F

    S. Kochsiek, F. Carollo, and I. Lesanovsky,Accelerating the approach of dissipative quantum spin systems towards stationarity through global spin rotations, Phys. Rev. A106, 012207 (2022)

    2022

  42. [50]

    Bao, and Z

    R. Bao, and Z. Hou,Accelerating relaxation in Markovian open quantum systems through quantum reset processes, arXiv:2212.11170

  43. [51]

    Ivander, N

    F. Ivander, N. Anto-Sztrikacs, and D. Segal,Hyperacceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment, Phys. Rev. E108, 014130 (2023). 11/14

    2023

  44. [52]

    Zhou, X.-D

    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. Research5, 043036 (2023)

    2023

  45. [53]

    Wang and J Wang,Mpemba effects in nonequilibrium open quantum systems, Phys

    X. Wang and J Wang,Mpemba effects in nonequilibrium open quantum systems, Phys. Rev. Research6, 033330 (2024)

    2024

  46. [54]

    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. A110, 042218 (2024)

    2024

  47. [55]

    Longhi,Photonic Mpemba effect, Opt

    S. Longhi,Photonic Mpemba effect, Opt. Lett.49, 5188 (2024)

    2024

  48. [56]

    Longhi,Bosonic Mpemba effect with non-classical states of light, APL Quantum1, 046110 (2024)

    S. Longhi,Bosonic Mpemba effect with non-classical states of light, APL Quantum1, 046110 (2024)

    2024

  49. [57]

    Boubakour, S

    M. Boubakour, S. Endo, T. Fogarty, and T. Busch,Dynamical invariant based shortcut to equilibration in open quantum systems, arXiv:2401.11659

    arXiv

  50. [58]

    M. E. Edo, L.-A. Wu,Study on quantum thermalization from thermal initial states in a superconducting quantum computer, arXiv:2403.14630

    arXiv

  51. [59]

    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

  52. [60]

    Longhi,Mpemba effect and super-accelerated thermalization in the damped quantum harmonic oscillator, arXiv:2411.09589

    S. Longhi,Mpemba effect and super-accelerated thermalization in the damped quantum harmonic oscillator, arXiv:2411.09589

    arXiv

  53. [61]

    Furtado and A

    J. Furtado and A. C. Santos, Strong Quantum Mpemba Effect with Squeezed Thermal Reservoirs, arXiv:2411.04545

    arXiv

  54. [62]

    D. Qian, H. Wang, and J. Wang,Intrinsic Quantum Mpemba Effect in Markovian Systems and Quantum Circuits, arXiv:2411.18417

  55. [63]

    Dong, H.F

    J.W. Dong, H.F. Mu, M. Qin, and H.T. Cui,Quantum Mpemba effect of Localization in the dissipative Mosaic model, arXiv:2411.03734

    arXiv

  56. [64]

    Medina, O

    I. Medina, O. Culhane, F. C. Binder, G. T. Landi, and J. Goold,Anomalous discharging of quantum batteries: the ergotropic Mpemba effect, arXiv:2412.13259

    arXiv

  57. [65]

    Kheirandish, N

    F. Kheirandish, N. Cheraghpour, and A. Moradian,The Mpemba effect in quantum oscillating and two-level systems, arXiv:2412.03943

    arXiv

  58. [66]

    J. Graf, J. Splettstoesser, and J. Monsel,Role of electron-electron interaction in the Mpemba effect in quantum dots, arXiv:2412.18456

    arXiv

  59. [67]

    Zatsarynna, A

    K. Zatsarynna, A. Nava, R. Egger, and A. Zazunov,Green’s Function Approach to Josephson Dot Dynamics and Application to Quantum Mpemba Effects, arXiv.2501.11609

    arXiv

  60. [68]

    Nava and R

    A. Nava and R. Egger,Mpemba effects in open nonequilibrium quantum systems, Phys. Rev. Lett.133, 136302 (2024)

    2024

  61. [69]

    D. J. Strachan, A. Purkayastha, S. R. Clark,Non-Markovian Quantum Mpemba effect, arXiv:2402.05756

  62. [70]

    Z.-M. Wang, S. L. Wu, M. S. Byrd, L.-A. Wu,Going beyond quantum Markovianity and back to reality: An exact master equation study, arXiv:2411.17197

    arXiv

  63. [71]

    J. M. Deutsch,Quantum statistical mechanics in a closed system, Phys. Rev. A43, 2046 (1991)

    1991

  64. [72]

    Srednicki,Chaos and quantum thermalization, Phys

    M. Srednicki,Chaos and quantum thermalization, Phys. Rev. E50, 888 (1994)

    1994

  65. [73]

    Rigol, V

    M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii,Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons, Phys. Rev. Lett.98, 050405 (2007)

    2007

  66. [74]

    Rigol, V

    M. Rigol, V. Dunjko, and M. Olshanii,Thermalization and its mechanism for generic isolated quantum systems, Nature452, 854 (2008)

    2008

  67. [75]

    F. Ares, S. Murciano, E. Vernier, and P. Calabrese,Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study, SciPost Phys.15, 089 (2023)

    2023

  68. [76]

    L. Kh. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, and M. K. Joshi,Observing the quantum Mpemba effect in quantum simulations, Phys. Rev. Lett.133, 010402 (2024). 12/14

    2024

  69. [77]

    Rylands, K

    C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Murciano, and B. BertiniMicroscopic origin of the quantum Mpemba effect in integrable systems, Phys. Rev. Lett.133, 010401 (2024)

    2024

  70. [78]

    Calabrese and J

    P. Calabrese and J. Cardy,Evolution of Entanglement Entropy in One-Dimensional Systems, J. Stat. Mech. (2005) P04010

    2005

  71. [79]

    Alba and P

    V. Alba and P. Calabrese,Entanglement and thermodynamics after a quantum quench in integrable systems, PNAS 114, 7947 (2017)

    2017

  72. [80]

    Alba and P

    V. Alba and P. Calabrese,Entanglement dynamics after quantum quenches in generic integrable systems, SciPost Phys.4, 017 (2018)

    2018

  73. [81]

    Murciano, F

    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

    2024

  74. [82]

    Klobas,Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: exact asymptotics in Rule 54, J

    K. Klobas,Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: exact asymptotics in Rule 54, J. Phys. A,57, 505001 (2024)

    2024

  75. [83]

    Rylands, E

    C. Rylands, E. Vernier and P. Calabrese,Dynamical symmetry restoration in the Heisenberg spin chain, J. Stat. Mech. (2024) 123102

    2024

  76. [84]

    Chalas, F

    K. Chalas, F. Ares, C. Rylands, and P. Calabrese,Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect, J. Stat. Mech. (2024) 103101

    2024

  77. [85]

    Yamashika, F

    S. Yamashika, F. Ares, and P. Calabrese,Entanglement asymmetry and quantum Mpemba effect in two- dimensional free-fermion systems, Phys. Rev. B110, 085126 (2024)

    2024

  78. [86]

    Ferro, F

    F. Ferro, F. Ares, and P. Calabrese,Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain, J. Stat. Mech. (2024) 023101

    2024

  79. [87]

    Yamashika, P

    S. Yamashika, P. Calabrese, and F. Ares,Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect, arXiv:2410.14299

    arXiv

  80. [88]

    Caceffo, S

    F. Caceffo, S. Murciano, and V. Alba,Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems, J. Stat. Mech. (2024) 063103

    2024

  81. [89]

    F. Ares, V. Vitale, and S. Murciano, The quantum Mpemba effect in free-fermionic mixed states, arXiv:2405.08913 (2024)

    2024 arXiv

  82. [90]

    Benini, V

    F. Benini, V. Godet, and A. H. Singh,Entanglement asymmetry in conformal field theory and holography, arXiv:2407.07969 (2024)

    2024

  83. [91]

    Banerjee, S

    T. Banerjee, S. Das, and K. Sengupta,Entanglement asymmetry in periodically driven quantum systems, arXiv:2412.03654 (2024)

    2024 arXiv

  84. [92]

    Turkeshi, P, Calabrese, and A

    X. Turkeshi, P, Calabrese, and A. De Luca,Quantum Mpemba Effect in Random Circuits, arXiv:2405.14514

    arXiv

  85. [93]

    Klobas, C

    K. Klobas, C. Rylands, and B. Bertini,Translation symmetry restoration under random unitary dynamics, arXiv:2406.04296

    arXiv

  86. [94]

    Liu, H.-K

    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)

    2024

  87. [95]

    Yu, Z.-X

    H. Yu, Z.-X. Li, S.-X. Zhang, Symmetry Breaking Dynamics in Quantum Many-Body Systems , arXiv:2501.13459

  88. [96]

    F. Ares, S. Murciano, P. Calabrese, and L. Piroli,Entanglement asymmetry dynamics in random quantum circuits arXiv:2501.12459

    arXiv

  89. [97]

    Liu, H.-K

    S. Liu, H.-K. Zhang, S. Yin, S.-X. Zhang, H. Yao,Quantum Mpemba effects in many-body localization systems, 2408.07750 (2024)

    2024

  90. [98]

    Foligno, P

    A. Foligno, P. Calabrese, and B. Bertini, Non-equilibrium dynamics of charged dual-unitary circuits, arXiv:2407.21786

    arXiv

  91. [99]

    Kells, D

    G. Kells, D. Meidan, and A. Romito,Topological transitions with continuously monitored free fermions, SciPost Phys.14, 031 (2023)

    2023

  92. [100]

    M. Fava, L. Piroli, T. Swann, D. Bernard, and A. Nahum,Nonlinear sigma models for monitored dynamics of free fermions, Phys. Rev. X13, 041045 (2023). 13/14

    2023

  93. [101]

    Poboiko, P

    I. Poboiko, P. Pöpperl, I. V. Gornyi, and A. D. Mirlin,Theory of Free Fermions under Random Projective Measurements, Phys. Rev. X13, 041046 (2023)

    2023

  94. [102]

    Skinner, J

    B. Skinner, J. Ruhman, and A. Nahum,Measurement-Induced Phase Transitions in the Dynamics of Entanglement, Phys. Rev. X9, 031009 (2019)

    2019

  95. [103]

    Y. Li, X. Chen, M. P. A. Fisher,Quantum Zeno Effect and the Many-body Entanglement Transition, Phys. Rev. B98, 205136 (2018)

    2018

  96. [104]

    A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith,Unitary-projective entanglement dynamics, Phys. Rev. B99, 224307 (2019)

    2019

  97. [105]

    Agrawal, A

    U. Agrawal, A. Zabalo, K. Chen, J. H. Wilson, A. C. Potter, J. H. Pixley, S. Gopalakrishnan, and R. Vasseur, Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits, Phys. Rev. X 12, 041002 (2022). 14/14

    2022

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Reviewed August 8, 2026 · model on record in the stance chip above.