{"id":"f2b1c2e6-2910-48cd-bba2-99bcc9ee0196","arxiv_id":"2502.08087","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":2.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"A review of the quantum Mpemba effect covering open and isolated quantum systems, key theories, experiments, and open questions.","lead":"This is a review of the quantum Mpemba effect, the phenomenon where a quantum system starting farther from equilibrium relaxes faster than one starting closer. It surveys the theoretical frameworks and experiments in both open and isolated quantum systems.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Claim of \"clearer, less controversial\" quantum Mpemba effects is not yet robust: most evidence uses a single probe, and the effect may be probe-dependent.","rationale":"The reader accepted this review with high confidence, and I agree that it is a competent synthesis with credible cited experiments. However, the weakest assumption that matters for the strongest claim is not only whether the cited experiments and derivations are correct, but whether the phenomenon they demonstrate is well-defined enough to support the comparative claim of being \"less controversial.\" The review's own text exposes a definitional fragility: the effect is defined relative to an arbitrary distance, the entanglement asymmetry is not a true distance to equilibrium, multiple crossings are acknowledged (Ref. 84), and the quasiparticle criterion of Ref. 77 is derived for the asymmetry rather than for general distances to the stationary state. The concrete test I propose would determine whether the crossing is robust across standard distance measures. If it is robust, the central claim survives and the existing accept is justified. If it is not, the paper should qualify its headline claim. I therefore recommend a conditional accept rather than an unconditional one, with the condition being an explicit discussion, or preferably a numerical check, of probe-independence. This is a scientific scope question, not a challenge to the authors' integrity or to the validity of the reviewed literature.","tokens_in":17837,"tokens_out":6269,"duration_ms":69759,"concrete_test":"Take the quenches analyzed in Ref. 81 (free-fermion XY chain) and in the quasiparticle criterion of Ref. 77, and for the same initial-state pairs compute, in addition to the Rényi-2 entanglement asymmetry, the trace distance and quantum relative entropy between ρ_A(t) and the asymptotic reduced state of the appropriate (generalized) Gibbs ensemble. If both alternative distances show the same persistent crossing and ordering, the probe-dependence concern is resolved. If either does not, the review should state that the quantum Mpemba effect is defined relative to the chosen distance, which weakens the \"less controversial\" claim. A computationally lighter variant is to compare, in the trapped-ion data of Ref. 76, the published asymmetry and Frobenius crossings against a trace-distance reconstruction from the same measured bit-string statistics.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's central comparative claim—that quantum manifestations of the Mpemba effect are \"less controversial\" and provide a \"clearer and more rigorous framework\" (Abstract/Introduction)—rests on treating crossings of a chosen distance as the signature of the effect. But the main distance used in isolated systems, the entanglement asymmetry (Box 1, Eq. 1), measures symmetry breaking, not distance to the stationary (generalized Gibbs) state. A state whose symmetry is restored rapidly can still be far from equilibrium, and vice versa. The asymmetry is non-monotonic in general, and the paper itself notes (Ref. 84) that multiple crossings can occur and that \"the existence of the quantum Mpemba effect cannot be inferred from the dynamics of the system at short times.\" This means the crossing criterion is already known to be fragile. What is not established is whether the effect is independent of the chosen probe: does the same pair of initial states show a persistent crossing when monitored with trace distance, relative entropy, or quantum fidelity to the stationary state? In the trapped-ion experiment (Ref. 76) both asymmetry and Frobenius distance showed the same qualitative behavior, which is encouraging, but that is one finite non-integrable system. For integrable systems and random circuits the effect is typically demonstrated with a single observable. If the ordering of relaxation depends on which distance one chooses, the claim that quantum Mpemba is \"less controversial\" is an artifact of a selected proxy rather than a robust property.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":18105,"tokens_out":4502,"duration_ms":43713,"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":[{"comment":"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.","section":"Introduction and Box 1"},{"comment":"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.","section":"Quantifying the distance from equilibrium and 'Further results in integrable systems'"},{"comment":"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.","section":"Outlook"}],"minor_comments":[{"comment":"The affiliation for SISSA reads 'T rieste'; it should be 'Trieste'.","section":"Author affiliations"},{"comment":"Reference 22 is missing a period after 'effect'; it reads 'A fresh understanding of the Mpemba effectNature Rev. Phys.'.","section":"References"},{"comment":"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.","section":"Figure 4"},{"comment":"The text uses 'Schrodinger' without the umlaut; standardize to 'Schrödinger'.","section":"Throughout"},{"comment":"Many entries are arXiv preprints that may have since appeared in journals; updating them would increase the usefulness of the review for readers.","section":"Reference list"}],"recommendation":"major_revision","confidential_remarks":"The review is written by leading authors in the field and will likely be influential. My main reservation concerns the strength of the comparative claim that quantum Mpemba effects are 'less controversial' and provide a 'more rigorous framework'; this claim needs to be tempered or supported by a discussion of probe dependence. I do not see grounds for rejection, but the requested changes are substantive enough to warrant a major revision rather than a minor one."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things upfront. First, this is an explicitly labeled review, not a new research contribution. Second, it is a good one: clearly organized, up to date, and unusually honest about what is not yet understood. I would send it to a serious referee, and I would expect it to become a standard entry point for people entering the field.\n\nWhat is actually new is the synthesis. The paper cleanly separates open from isolated systems, and within isolated systems it distinguishes integrable from chaotic dynamics. That framing is not novel in itself, but it is executed better than in the scattered papers it cites. The box on distance measures is genuinely useful, as is the summary of the quasiparticle picture for integrable quenches. The authors also deserve credit for flagging open questions, especially the lack of a general criterion for ergodic systems and the unexplored monitored-circuit setting. The coverage of experiments (trapped-ion, single-qubit, and the 12-ion simulator) is accurate as far as I can tell from the published literature.\n\nWhere are the soft spots? The main one is the introductory claim that quantum manifestations are 'less controversial' and provide a 'clearer and more rigorous framework.' That is an editorial opinion, and it rests on a narrower basis than the sentence suggests. The crossing criterion that defines the effect in most of the review is probe-dependent: the entanglement asymmetry measures symmetry restoration, not distance to the stationary state, and the review itself cites Ref. 84 showing that multiple crossings can occur and that short-time dynamics are not reliable. The trapped-ion experiment checked both asymmetry and Frobenius distance and saw the same behavior, which is encouraging, but that is one non-integrable system. For integrable models and random circuits the evidence is mostly single-probe. So the 'less controversial' claim is somewhat ahead of the evidence. The paper would be improved by a sentence acknowledging that the effect is defined relative to a chosen distance and that probe-independence is still being tested.\n\nA second, minor point: the review leans heavily on the authors' own results. That is not a flaw here, because those results are independently published and experimentally tested. But newcomers should be aware that the entanglement-asymmetry tool is the authors' home turf, and the review does not spend much space on alternative quantities like fidelity or trace distance to the GGE in the isolated case.\n\nBottom line: this is a solid, useful review. It deserves peer review and publication. I would suggest that the editors ask the authors to temper the 'less controversial' sentence and add a caveat about probe dependence. That is a revision, not a rejection.","headline":"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.","tokens_in":18583,"tokens_out":1293,"would_cite":true,"duration_ms":14553,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["quantum Mpemba effect","entanglement asymmetry","open quantum systems","quantum quench","integrability","symmetry restoration","Lindblad dynamics","non-equilibrium relaxation"],"falsifier":"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.","tokens_in":1632,"feed_emoji":"🧊","tokens_out":1755,"duration_ms":544307,"temperature":0.7,"pith_summary":"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.","feed_headline":"Quantum Mpemba effects are real — and cleaner than water","feed_subtitle":"A farther-from-equilibrium quantum state can relax faster than a nearer one; trapped-ion experiments confirm it.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"defines the entanglement asymmetry used to quantify symmetry breaking and its restoration after quenches","marker":"[33]"},{"why":"establishes that a unitary rotation of the initial state can suppress the slowest Lindblad eigenmode, giving the strong Mpemba effect in Markovian open systems","marker":"[42]"},{"why":"reports the trapped-ion experiment observing the strong quantum Mpemba effect in an open system","marker":"[43]"},{"why":"reports the trapped-ion qubit experiment observing the inverse Mpemba effect and its strong version","marker":"[47]"},{"why":"reports the 12-ion quantum-simulator experiment observing the symmetry-restoration Mpemba effect in an isolated system","marker":"[76]"},{"why":"derives the quasiparticle-based microscopic mechanism and necessary and sufficient conditions for the effect in integrable systems","marker":"[77]"},{"why":"provides the free-energy thermodynamic framework for detecting the Mpemba effect in thermalizing open systems","marker":"[32]"},{"why":"supplies the classical Markovian Mpemba theory whose eigenmode logic the quantum open-system results extend","marker":"[19]"}],"fun_headline_variants":["Quantum Mpemba: Hotter states equilibrate faster","Farther from equilibrium? Relax faster in quantum systems","When quantum hot cools faster than cold: Mpemba effect","Trapped ions confirm quantum Mpemba effect","Two sides of quantum Mpemba: open and isolated"],"cache_read_input_tokens":20736,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Quantum Mpemba: Hotter states equilibrate faster","Farther from equilibrium? Relax faster in quantum systems","When quantum hot cools faster than cold: Mpemba effect","Trapped ions confirm quantum Mpemba effect","Two sides of quantum Mpemba: open and isolated"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000298,"raw_usage":{"total_tokens":1673,"prompt_tokens":838,"completion_tokens":835,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":454,"completion_tokens_details":{"reasoning_tokens":754}},"tokens_in":454,"tokens_out":835,"duration_ms":10819,"temperature":1.0,"reasoning_tokens":754,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T10:29:10.608428+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"defines the entanglement asymmetry used to quantify symmetry breaking and its restoration after quenches"},{"cited_title":"Carollo, A","cited_arxiv_id":null,"evidence_quote":"establishes that a unitary rotation of the initial state can suppress the slowest Lindblad eigenmode, giving the strong Mpemba effect in Markovian open systems"},{"cited_title":"Zhang, G","cited_arxiv_id":null,"evidence_quote":"reports the trapped-ion experiment observing the strong quantum Mpemba effect in an open system"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reports the trapped-ion qubit experiment observing the inverse Mpemba effect and its strong version"},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"reports the 12-ion quantum-simulator experiment observing the symmetry-restoration Mpemba effect in an isolated system"},{"cited_title":"Rylands, K","cited_arxiv_id":null,"evidence_quote":"derives the quasiparticle-based microscopic mechanism and necessary and sufficient conditions for the effect in integrable systems"},{"cited_title":"Moroder, O","cited_arxiv_id":null,"evidence_quote":"provides the free-energy thermodynamic framework for detecting the Mpemba effect in thermalizing open systems"}],"review_version":1}