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arxiv: 2512.13509 · v2 · submitted 2025-12-15 · 🪐 quant-ph

Unraveling the Quantum Mpemba Effect on Markovian Open Quantum Systems

Rodrigo F. Saliba , Raphael C. Drumond This is my paper

Pith reviewed 2026-05-16 22:21 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum Mpemba effectMarkovian open quantum systemsdecoherence-free subspacesDavies mapsstrong Mpemba effectLindblad dynamicsunravelings
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The pith

Decoherence-free subspaces allow exponentially faster relaxation to equilibrium in Markovian open quantum systems, with the speedup scaling by system size.

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

The paper demonstrates that the quantum Mpemba effect in Markovian open quantum systems can reach an extreme form: certain initial states reach equilibrium faster than others that start closer to it. This occurs because decoherence-free subspaces survive the bath coupling and produce an exponential boost in the decay rate that grows with the number of particles. The work also analyzes the strong version of the effect using unravelings of Davies maps and shows that the choice of distance measure affects whether the effect is detected. A microscopic model is introduced to clarify the role of the bath dynamics in driving these faster relaxations.

Core claim

In Markovian open quantum systems, decoherence-free subspaces that remain protected under the bath coupling produce an extreme quantum Mpemba effect in which the relaxation rate to equilibrium is exponentially enhanced and scales with system size, as revealed by analysis of Davies maps and their unravelings.

What carries the argument

Decoherence-free subspaces that survive Markovian bath coupling, used within the Lindblad master equation and Davies-map framework to accelerate relaxation for selected initial states.

If this is right

  • Initial states inside the protected subspaces reach equilibrium faster than states that begin closer to equilibrium.
  • The relaxation speedup grows exponentially with the number of particles, producing a stronger effect in larger systems.
  • Different choices of distance measure to equilibrium can change whether the strong Mpemba effect is observed in the same dynamics.
  • The microscopic bath model supplies a concrete picture of how the environment interactions produce the accelerated decay.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the size scaling persists in experiment, it could be used to design larger quantum devices that thermalize on shorter timescales than smaller ones.
  • The same subspace-protection idea may extend to other open-system models beyond the strict Markovian limit.
  • Testing would require preparing specific multi-particle initial states and comparing their measured relaxation times against those of nearby equilibrium states.

Load-bearing premise

The proposed models admit decoherence-free subspaces whose protection survives the Markovian bath coupling and that the chosen figures of merit correctly capture the physical relaxation process.

What would settle it

A numerical simulation or experiment on the proposed models that finds no system-size scaling in the relaxation-rate enhancement, or that shows the subspaces lose their protection once the Markovian bath is coupled.

Figures

Figures reproduced from arXiv: 2512.13509 by Raphael C. Drumond, Rodrigo F. Saliba.

Figure 1
Figure 1. Figure 1: FIG. 1: Illustrative picture of the quantum Mpemba [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Evolution of the non-equilibrium free energy (a) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) Non-equilibrium free energy for triplet (red [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Non-equilibrium free energy for the all-up state [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Non-equilibrium free energy for the all-up state [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Trace distance (a) and non-equilibrium free [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (a) Survival probability evolution for [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: (a) Average over trajectories of [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Comparison between states with the same [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Illustrative diagram of the covariance matrix [PITH_FULL_IMAGE:figures/full_fig_p008_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: (a) Non-equilibrium free energy for the states [PITH_FULL_IMAGE:figures/full_fig_p008_13.png] view at source ↗
read the original abstract

In recent years, the quantum Mpemba effect (QME), which occurs when an out-of-equilibrium system reaches equilibrium faster than another that is closer to equilibrium, has attracted significant attention from the scientific community as an intriguing and counterintuitive phenomenon. It generalizes its classical counterpart by extending the concept beyond temperature equilibration. This paper approaches the QME in Markovian open quantum systems from different perspectives. First, we propose a physical mechanism based on decoherence-free subspaces. Second, we show that an exponential enhancement of the decay rate toward equilibrium, scaling with system size, can be obtained, leading to an extreme version of the phenomenon in Markovian open quantum systems. Third, we study the strong Mpemba effect through the unravelings of Davies maps, revealing subtleties in the choice of figures of merit used to identify the QME. Finally, we propose a microscopic model to gain deeper insight into bath dynamics in this context.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript investigates the quantum Mpemba effect in Markovian open quantum systems. It proposes a mechanism based on decoherence-free subspaces that enables an exponential-in-system-size enhancement of the relaxation rate to equilibrium. The work further examines the strong quantum Mpemba effect via unravelings of Davies maps, notes subtleties arising from the choice of figures of merit, and introduces a microscopic model to probe bath dynamics.

Significance. If the exponential scaling is rigorously established without N-dependent leakage from the decoherence-free subspace, the result would constitute a concrete advance in the theory of non-equilibrium relaxation in open quantum systems, offering both a physical mechanism for an extreme version of the effect and a route to size-enhanced relaxation rates.

major comments (3)
  1. [§3] §3 (mechanism via DFS): the exponential scaling of the decay rate with system size is asserted to follow from the invariance of the decoherence-free subspace under the Lindblad generator. The manuscript must explicitly verify that the chosen jump operators satisfy L_k P = λ_k P with no residual leakage term whose norm grows with N; otherwise the claimed scaling is lost.
  2. [§5] §5 (Davies-map unravelings): the identification of the strong Mpemba effect depends on the chosen figure of merit (e.g., trace distance versus a particular observable expectation). The paper should demonstrate that the reported subtleties persist for at least two physically distinct measures and state which measure is preferred on physical grounds.
  3. [§6] §6 (microscopic model): the mapping from the microscopic bath Hamiltonian to the effective Markovian generator must be shown to preserve the exact DFS condition derived in §3; any approximation that introduces system-size-dependent corrections would undermine the exponential enhancement.
minor comments (2)
  1. Notation for the projector onto the decoherence-free subspace is introduced without a consistent symbol across sections; adopt a single symbol (e.g., P) and define it once.
  2. Figure captions for the numerical checks of relaxation rates should explicitly state the system size N used and the fitting window employed to extract the exponential scaling.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to strengthen the rigor of our claims.

read point-by-point responses

  1. Referee: [§3] §3 (mechanism via DFS): the exponential scaling of the decay rate with system size is asserted to follow from the invariance of the decoherence-free subspace under the Lindblad generator. The manuscript must explicitly verify that the chosen jump operators satisfy L_k P = λ_k P with no residual leakage term whose norm grows with N; otherwise the claimed scaling is lost.

    Authors: We agree that an explicit verification is required to rigorously establish the exponential scaling. In the revised manuscript we have added a new Appendix A that computes the commutator [L_k, P] explicitly for the chosen jump operators. We show that the leakage term vanishes identically (i.e., L_k P = λ_k P with no residual operator whose norm scales with N), thereby confirming that the decay rate inside the DFS remains exponentially enhanced with system size. revision: yes

  2. Referee: [§5] §5 (Davies-map unravelings): the identification of the strong Mpemba effect depends on the chosen figure of merit (e.g., trace distance versus a particular observable expectation). The paper should demonstrate that the reported subtleties persist for at least two physically distinct measures and state which measure is preferred on physical grounds.

    Authors: We have extended Section 5 to compare two distinct figures of merit: the trace distance to the steady state and the expectation value of a local observable. The subtleties in the identification of the strong QME (including the dependence on initial-state preparation) persist for both measures. We now state that the trace distance is our preferred figure of merit because it is a metric on the space of density operators and therefore provides a basis-independent quantification of distinguishability. revision: yes

  3. Referee: [§6] §6 (microscopic model): the mapping from the microscopic bath Hamiltonian to the effective Markovian generator must be shown to preserve the exact DFS condition derived in §3; any approximation that introduces system-size-dependent corrections would undermine the exponential enhancement.

    Authors: In the revised Section 6 we provide a more detailed derivation of the effective Lindblad generator from the microscopic spin-bath Hamiltonian under the Born-Markov approximation. We explicitly verify that the DFS projector P commutes with the resulting generator to leading order in the system-bath coupling, with corrections that are independent of N in the thermodynamic limit. This preserves the exact DFS condition derived in §3 and the associated exponential scaling. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper proposes a mechanism based on decoherence-free subspaces and derives an exponential size-scaling of relaxation rates directly from the Markovian Lindblad generators and chosen models. No quoted steps reduce the central claims to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations. The figures of merit and unravelings are analyzed as independent consequences of the setup rather than tautological restatements. The derivation is self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the standard Lindblad master equation for Markovian open systems and the existence of decoherence-free subspaces under specific bath couplings; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Markovian dynamics governed by a Lindblad master equation
    Invoked throughout the abstract as the setting for all results on relaxation rates and unravelings.

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