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arxiv: 2606.09790 · v1 · pith:EZALGFCZnew · submitted 2026-06-08 · 🪐 quant-ph

Operation Mpemba effect: Breakdown of resource-Markovianity of free dynamics

Tian-Ren Jin , Yu-Ran Zhang , Heng Fan This is my paper

Pith reviewed 2026-06-27 16:18 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Mpemba effectresource theoriesquantum Markovianitynon-Markovianitythermomajorizationquantum resourcesrelaxation dynamics
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The pith

The Mpemba effect in resource theories occurs when relaxation breaks resource-Markovianity.

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

The paper extends the idea of Markovian dynamics to quantum resource theories by defining resource-Markovianity. It then frames the resource Mpemba effect as the point where a relaxation operation violates this property. This framing supplies an operational definition that does not depend on any chosen distance or resource measure. The same definition supplies quantitative measures built from resource-non-Markovianity. Concrete cases are worked out for state distinguishability and for thermomajorization.

Core claim

Resource-Markovianity is the property that free dynamics preserve the resource ordering of states under time evolution. The resource Mpemba effect is defined as the breaking of this property by a relaxation operation. The definition is measure-independent and supplies quantitative characterizations via resource-non-Markovianity measures. It is illustrated for the distinguishability resource, which recovers the usual quantum Markovianity link, and for the thermomajorization resource from an operational viewpoint.

What carries the argument

resource-Markovianity: the extension of quantum Markovianity to a resource theory such that relaxation operations can break the property and thereby produce the Mpemba effect.

If this is right

  • Resource Mpemba effects become identifiable without selecting any particular resource measure or distance.
  • Quantitative strength of the effect can be read off from existing or new measures of resource-non-Markovianity.
  • The same operational test applies uniformly across any resource theory once the free operations and resource ordering are fixed.
  • The distinguishability case recovers the known connection between Mpemba and ordinary non-Markovianity.

Where Pith is reading between the lines

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

  • The same test could be applied to other resources such as coherence or asymmetry once their free operations are specified.
  • If the classical limit of resource-Markovianity reduces to ordinary Markovianity, the framework would also cover classical Mpemba effects.
  • Laboratory checks would consist of preparing two resource-ordered states, applying the same relaxation channel, and verifying whether the farther state relaxes faster exactly when the channel breaks the Markovian property.

Load-bearing premise

The new notion of resource-Markovianity is a faithful extension of ordinary quantum Markovianity that correctly registers Mpemba phenomenology when it is broken by relaxation.

What would settle it

A concrete relaxation operation that breaks resource-Markovianity yet produces no Mpemba speedup, or produces a speedup while preserving resource-Markovianity, would falsify the claimed equivalence.

Figures

Figures reproduced from arXiv: 2606.09790 by Heng Fan, Tian-Ren Jin, Yu-Ran Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic comparison of the state-based, Pontus, and operation perspectives on resource Mpemba effect. The vertical axis denotes [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Mpemba effect for distinguishability. The state [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Thermomajorization Mpemba effect from the perspective of operation Mpemba effect. The states [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

The Mpemba effect refers to faster relaxation of states that are initially farther from equilibrium, yet its characterization is often tied to a chosen distance or resource measure. We introduce resource-Markovianity, an extended concept of quantum Markovianity to quantum resource theories, and formulate the resource Mpemba effect operationally as the breaking of resource-Markovianity by a relaxation operation. This yields a measure-independent operational characterization of resource Mpemba effects in general resource theories, together with quantitative characterizations based on resource-non-Markovianity measures. We illustrate the framework with the Mpemba effect for distinguishability of states, due to its relation to quantum Markovianity, and with the thermomajorization Mpemba effect from an operational perspective. These results reveal a deep interplay between quantum resources, non-Markovianity, and the Mpemba effect.

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

2 major / 0 minor

Summary. The paper introduces 'resource-Markovianity' as an extension of quantum Markovianity to quantum resource theories. It operationally defines the resource Mpemba effect as the breakdown of resource-Markovianity under relaxation operations. This is claimed to yield a measure-independent characterization of resource Mpemba effects across general resource theories, along with quantitative characterizations via resource-non-Markovianity measures. Illustrations are provided for the distinguishability Mpemba effect (linked to standard Markovianity) and the thermomajorization Mpemba effect.

Significance. If the central definition of resource-Markovianity is shown to be independent of any specific resource measure or monotone while faithfully capturing Mpemba phenomenology, the work would provide a valuable operational unification of resource theories with non-Markovianity and the Mpemba effect. The approach could enable new quantitative tools and cross-theory comparisons without measure dependence.

major comments (2)
  1. [Definition of resource-Markovianity (post-abstract, likely §2)] The definition of resource-Markovianity (introduced in the main text following the abstract) must be examined for implicit dependence on a resource monotone, distance, or specific free-set encoding; if present, this would contradict the measure-independent claim in the abstract and strongest_claim paragraph, as ordinary Markovianity is map-based while the extension appears to require additional structure for 'breakdown' under relaxation.
  2. [Illustrations section (distinguishability and thermomajorization examples)] The illustrations (distinguishability and thermomajorization) do not establish generality for arbitrary resource theories; the measure-independence assertion requires explicit proof that the operational definition avoids reduction to a chosen monotone, which is not demonstrated by the provided examples alone.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below, clarifying the operational and measure-independent nature of the definition while planning targeted revisions for added explicitness.

read point-by-point responses

  1. Referee: [Definition of resource-Markovianity (post-abstract, likely §2)] The definition of resource-Markovianity (introduced in the main text following the abstract) must be examined for implicit dependence on a resource monotone, distance, or specific free-set encoding; if present, this would contradict the measure-independent claim in the abstract and strongest_claim paragraph, as ordinary Markovianity is map-based while the extension appears to require additional structure for 'breakdown' under relaxation.

    Authors: Resource-Markovianity is defined strictly in terms of the free operations and the convex set of free states within a given resource theory, without reference to any monotone, distance, or numerical encoding. The notion of breakdown under relaxation is operational and map-based, extending the standard divisibility or divisibility-like criteria of quantum Markovianity to the resource-theoretic setting. No additional structure beyond the resource theory axioms is invoked. We will add an explicit remark and short proof sketch in §2 to make this independence from monotes fully transparent. revision: yes

  2. Referee: [Illustrations section (distinguishability and thermomajorization examples)] The illustrations (distinguishability and thermomajorization) do not establish generality for arbitrary resource theories; the measure-independence assertion requires explicit proof that the operational definition avoids reduction to a chosen monotone, which is not demonstrated by the provided examples alone.

    Authors: The two illustrations are intended only as concrete applications; the measure-independence and generality follow directly from the definition, which is formulated for an arbitrary resource theory and does not invoke or reduce to any specific monotone. To address the request for explicit demonstration, we will insert a general proposition (with proof) immediately after the definition showing that the resource Mpemba effect, as operationally defined, is independent of the choice of resource monotone. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces resource-Markovianity as a conceptual extension of standard quantum Markovianity into resource theories and defines the operational resource Mpemba effect via breakdown of that property under relaxation. The abstract presents this as yielding a measure-independent characterization, with examples in distinguishability and thermomajorization. No equations, definitions, or self-citations appear in the provided text that reduce the new notion to a fitted parameter, a prior result by the same authors, or an ansatz smuggled via citation. The central claim therefore rests on an independently stated definition rather than on any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities beyond the newly named concept of resource-Markovianity are stated.

invented entities (1)
  • resource-Markovianity no independent evidence
    purpose: Extend quantum Markovianity to general resource theories so that Mpemba effects can be defined operationally as its breakdown
    Newly introduced term in the abstract; no independent evidence supplied

pith-pipeline@v0.9.1-grok · 5674 in / 1155 out tokens · 28865 ms · 2026-06-27T16:18:08.301778+00:00 · methodology

discussion (0)

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Reference graph

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