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arxiv: 2604.14740 · v2 · submitted 2026-04-16 · 🪐 quant-ph

Quantum Mpemba Effect in Non-Equilibrium Quantum Thermometry

Zi-Shen Li , Yuxiang Yang This is my paper

Pith reviewed 2026-05-10 11:35 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum Mpemba effectquantum thermometrynon-equilibrium dynamicsMarkovian thermalizationquantum Fisher informationopen quantum systems
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0 comments X p. Extension

The pith

Optimal initial states for early-stage quantum thermometry exhibit the quantum Mpemba effect and reach equilibrium faster than most other states.

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

The paper establishes that in Markovian open quantum systems, the initial states maximizing precision in temperature estimation during the initial phase of thermalization also display the quantum Mpemba effect. These states, despite starting farther from equilibrium, thermalize more rapidly than the average over random initial states. This creates a direct link between the practical goal of accurate non-equilibrium thermometry and an anomalous relaxation process, showing that the best probes for sensing temperature can do so while equilibrating quicker.

Core claim

In a Markovian model, the initial states that are optimal for thermometry exhibit QMpE with high probability and thermalize faster than most initial states.

What carries the argument

The optimization of initial states for quantum Fisher information in temperature estimation under Markovian thermalization dynamics, which selects states that also satisfy the faster relaxation condition of the quantum Mpemba effect.

If this is right

  • Temperature estimation protocols can select initial states that both maximize precision and shorten the required equilibration time.
  • Quantum thermometers can be designed to operate in regimes where anomalous relaxation improves overall performance.
  • The link implies that precision in early-stage sensing correlates with faster approach to the thermal state for most optimal choices.

Where Pith is reading between the lines

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

  • Similar optimization might be tested in non-Markovian environments to check whether the Mpemba-thermometry connection persists beyond memoryless baths.
  • This could extend to other estimation tasks where faster relaxation of the probe state is desirable for repeated measurements.
  • Engineering initial states with Mpemba properties may offer a general strategy for accelerating quantum information protocols that involve thermalization.

Load-bearing premise

The open quantum system follows memoryless Markovian dynamics and temperature estimation is restricted to the early stage of thermalization.

What would settle it

A concrete counterexample in which the optimal thermometry initial state does not thermalize faster than the majority of random states under the same Markovian master equation would disprove the claim.

Figures

Figures reproduced from arXiv: 2604.14740 by Yuxiang Yang, Zi-Shen Li.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic illustration of QMpE and thermometry. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Conceptual illustration of the main result: ther [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Numerical results. (a) The trace distance between [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Spectrum of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

The quantum Mpemba effect (QMpE) describes an anomalous thermalization phenomenon in which quantum states initially far from equilibrium can approach thermal equilibrium faster than states that begin closer to it. While this effect has been extensively studied in various frameworks, its practical implications for quantum information processing remain largely unexplored. We investigate the relationship between QMpE and quantum thermometry, focusing on non-equilibrium scenarios where measurements are performed during early-stage thermalization. In a Markovian model, we rigorously prove that the initial states that are optimal for thermometry exhibit QMpE with high probability and thermalize faster than most initial states. Our results reveal a fundamental connection between quantum thermodynamics and thermometry, suggesting that QMpE can be harnessed to enhance temperature estimation with quantum probes.

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

0 major / 4 minor

Summary. The manuscript investigates the relationship between the quantum Mpemba effect (QMpE) and non-equilibrium quantum thermometry. In an explicitly Markovian open quantum system, it claims a rigorous proof that initial states optimal for thermometry—defined via maximization of the early-time quantum Fisher information—exhibit the QMpE with high probability and thermalize faster than most other initial states. The work highlights potential applications for improving temperature estimation using quantum probes during early thermalization.

Significance. If the central proof holds, the result is significant for establishing a concrete link between anomalous thermalization and optimal quantum metrology. It suggests that states selected for thermometry performance can simultaneously benefit from faster relaxation via the QMpE, providing a strategy to enhance sensing speed in non-equilibrium regimes. The explicit Markovian setting makes the claim falsifiable and internally consistent; the focus on early-time dynamics aligns well with practical thermometry constraints. The rigorous mathematical derivation within the model is a clear strength.

minor comments (4)
  1. The abstract is concise, but the introduction would benefit from a brief comparison to classical Mpemba effect studies to better contextualize the quantum extension.
  2. In the definition of optimality (around Eq. (7)), the early-time cutoff for the quantum Fisher information should be justified more explicitly with respect to the system-bath coupling strength.
  3. Figure 2: The relaxation curves for optimal versus random states are clear, but including an inset with the probability distribution over the ensemble would strengthen the 'high probability' and 'faster than most' claims.
  4. A few instances of undefined notation appear in Section 4; adding a short notation table would improve readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the positive assessment of its significance in linking the quantum Mpemba effect to non-equilibrium quantum thermometry. The recommendation for minor revision is noted. However, the report contains no specific major comments requiring point-by-point response.

Circularity Check

0 steps flagged

No significant circularity; derivation is a self-contained Markovian proof

full rationale

The paper's central result is a rigorous mathematical proof inside an explicitly Markovian open-system model: optimal initial states for early-time quantum Fisher information thermometry are shown to exhibit the quantum Mpemba effect and faster thermalization than generic states. No load-bearing step reduces by construction to a fitted parameter, self-defined quantity, or prior self-citation chain. The Markovian assumption and early-stage restriction are declared upfront rather than smuggled; the implication from optimality to faster relaxation follows from the model's dynamics without renaming known results or importing uniqueness theorems from the authors' own prior work. The derivation therefore remains independent of its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the Markovian dynamics assumption and the definition of optimality for thermometry; no free parameters or new entities are mentioned.

axioms (1)
  • domain assumption The open quantum system follows Markovian dynamics.
    Explicitly stated as the model in which the proof is carried out.

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Reference graph

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