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arxiv: 2605.27369 · v1 · pith:S4R6QDSFnew · submitted 2026-05-26 · 🪐 quant-ph

Generalized multilevel amplitude damping channels and their thermodynamic performances

Vito Vetrano , Vittorio Giovannetti , Vasco Cavina This is my paper

Pith reviewed 2026-06-29 17:10 UTC · model grok-4.3

classification 🪐 quant-ph
keywords generalized multilevel amplitude dampingergotropic capacitanceMarkovian Mpemba effectquantum thermodynamicsqudit channelswork extractionthermal decoherencecoherent ergotropy
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The pith

GMAD channels show ergotropic capacitance is non-monotonic in bath temperature and produce a Markovian Mpemba effect under iteration.

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

The paper defines a family of generalized multilevel amplitude damping channels to describe how a qudit loses coherence and energy when coupled to a thermal bath. It measures the resulting loss of usable work by tracking ergotropic capacitance together with separate coherent and incoherent contributions. The central results are that this capacitance does not rise or fall steadily as bath temperature changes and that repeated application of the channel can cause the ergotropic values at two different temperatures to cross. These behaviors matter because they alter the best strategy for preparing a qudit to retain extractable work in a realistic thermal setting.

Core claim

The ergotropic capacitance of a GMAD channel is not monotonic in the temperature of the environment; moreover, iterating the map can lead to crossings between ergotropic functionals at different temperatures, indicating the presence of a Markovian Mpemba effect.

What carries the argument

The GMAD channel family, a parameterized set of completely positive maps that generalize amplitude damping to multilevel systems while incorporating thermal equilibrium states, used to compute work functionals and separate coherent versus incoherent ergotropy.

If this is right

  • Optimal initial states for a qudit in a thermal environment can be chosen to maximize retained work extraction value.
  • The non-monotonic dependence on temperature implies that an intermediate bath temperature can preserve more ergotropy than either a colder or hotter bath.
  • Repeated application of the channel produces crossings, so the ordering of work-extraction performance at two temperatures can reverse after sufficient noise steps.
  • New quantifiers separate the coherent and incoherent parts of ergotropy, allowing finer diagnosis of which resource is lost first.

Where Pith is reading between the lines

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

  • The observed crossings suggest that protocols relying on thermal relaxation steps might sometimes benefit from waiting longer rather than shorter times at fixed temperature.
  • The same non-monotonicity could appear in other noise models that interpolate between zero-temperature damping and full thermalization.
  • Device calibration routines that assume monotonic resource loss with temperature may need revision when operating near the crossing points.

Load-bearing premise

The chosen mathematical form of the GMAD family is assumed to correctly capture the physical coupling of a qudit to a thermal bath.

What would settle it

A laboratory measurement on a physical qudit that shows ergotropic capacitance rising or falling steadily with bath temperature, or that shows no crossing of ergotropic curves after repeated applications of the noise map.

Figures

Figures reproduced from arXiv: 2605.27369 by Vasco Cavina, Vito Vetrano, Vittorio Giovannetti.

Figure 1
Figure 1. Figure 1: FIG. 1. Qualitative sketch of the effect of the GMAD chan [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (From top left to center right) 1-cell shell-maximal [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Ratios between the coherent ergotropy (green [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Depiction of the level structure of the environment [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. .The unitary evolution under [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original abstract

We introduce a new class of quantum channels, the Generalized Multilevel Amplitude Damping (GMAD) channels, to model noise and decoherence effects in a qudit coupled to a thermal environment. The degradation of energetic resources under GMADs is investigated by evaluating work functionals and ergotropic capacitances, with particular attention to the coherent and incoherent contributions to ergotropy, for which we introduce new quantifiers. Our analysis sheds light on how to optimally prepare a qudit in a thermal environment in order to preserve its value from the perspective of work extraction, and reveals several counterintuitive phenomena: the ergotropic capacitance of a GMAD channel is not monotonic in the temperature of the environment; moreover, iterating the map can lead to crossings between ergotropic functionals at different temperatures, indicating the presence of a Markovian 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 / 2 minor

Summary. The paper introduces Generalized Multilevel Amplitude Damping (GMAD) channels as a model for noise on a qudit coupled to a thermal environment. It evaluates the degradation of energetic resources via work functionals and ergotropic capacitances, defines new quantifiers separating coherent and incoherent ergotropy contributions, and reports that ergotropic capacitance is non-monotonic in bath temperature while iterated applications produce crossings between ergotropic functionals at different temperatures, interpreted as a Markovian Mpemba effect.

Significance. If the GMAD family is accepted as a faithful thermal-noise model, the reported non-monotonicity and Mpemba crossings would constitute concrete, falsifiable predictions about resource preservation under iterated thermal maps, extending known single-qubit results to multilevel systems. The new ergotropy quantifiers are a modest but useful addition to the quantum-thermodynamics toolkit. The absence of a microscopic derivation, however, confines the significance to the mathematical properties of the chosen parametrization rather than generic thermal physics.

major comments (2)
  1. [Introduction / channel definition (abstract and opening sections)] The central claims (non-monotonic ergotropic capacitance and Markovian Mpemba crossings) rest on the assertion that GMAD channels faithfully represent coupling to a thermal bath. The manuscript introduces the channel family by direct definition of its Kraus operators and temperature-dependent rates without supplying a system-bath Hamiltonian, weak-coupling limit, or Born-Markov derivation that would fix the functional form of those rates. This modeling choice is load-bearing: any observed non-monotonicity could be an artifact of the ad-hoc parametrization rather than a generic feature of thermal noise.
  2. [Sections presenting the ergotropic capacitance and iteration results] The thermodynamic performance analysis (work extraction, ergotropic capacitance) is performed exclusively on the GMAD family as defined; no comparison is provided to standard amplitude-damping or generalized amplitude-damping channels whose rates do arise from microscopic models. Without such a benchmark, it is unclear whether the reported counter-intuitive phenomena survive under physically derived rate equations.
minor comments (2)
  1. [Definitions of new quantifiers] Notation for the new coherent/incoherent ergotropy quantifiers should be introduced with explicit equations and contrasted with existing ergotropy decompositions in the literature.
  2. [Figures] Figure captions and axis labels for any plots of ergotropic capacitance versus temperature or iteration number should explicitly state the dimension of the qudit and the precise GMAD parameters used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The two major comments raise valid points about the modeling assumptions and the need for benchmarks. We address each below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: The central claims (non-monotonic ergotropic capacitance and Markovian Mpemba crossings) rest on the assertion that GMAD channels faithfully represent coupling to a thermal bath. The manuscript introduces the channel family by direct definition of its Kraus operators and temperature-dependent rates without supplying a system-bath Hamiltonian, weak-coupling limit, or Born-Markov derivation that would fix the functional form of those rates. This modeling choice is load-bearing: any observed non-monotonicity could be an artifact of the ad-hoc parametrization rather than a generic feature of thermal noise.

    Authors: We agree that the absence of a microscopic derivation limits the claim to a specific family of channels. The GMAD Kraus operators and rates are constructed phenomenologically to generalize the qubit amplitude-damping channel while enforcing that the Gibbs state is a fixed point and satisfying detailed balance. This ensures thermodynamic consistency by design, but the functional form of the rates is not derived from a system-bath Hamiltonian in the manuscript. We will revise the introduction and channel-definition section to state explicitly that GMAD is a phenomenological model, to discuss its reduction to standard thermal maps in the qubit limit, and to note that the reported non-monotonicity and Mpemba crossings are properties of this parametrization rather than proven generic features of all thermal noise. revision: partial

  2. Referee: The thermodynamic performance analysis (work extraction, ergotropic capacitance) is performed exclusively on the GMAD family as defined; no comparison is provided to standard amplitude-damping or generalized amplitude-damping channels whose rates do arise from microscopic models. Without such a benchmark, it is unclear whether the reported counter-intuitive phenomena survive under physically derived rate equations.

    Authors: We accept that an explicit benchmark would strengthen the manuscript. For dimension d=2 the GMAD channel coincides with the standard temperature-dependent amplitude-damping channel whose rates follow from the usual thermal detailed-balance condition. We will add a short subsection (or appendix) that recomputes the ergotropic capacitance for the qubit case using the standard microscopic rate expressions and verifies that the non-monotonicity persists. For d>2 we will note that no universally accepted microscopic derivation of generalized amplitude damping exists in the literature, so a direct comparison is not currently possible; we will flag this as a limitation and suggest that the observed phenomena motivate future microscopic studies. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are direct computations on explicitly defined GMAD channels and new ergotropic quantifiers.

full rationale

The paper defines the GMAD channel family and introduces new quantifiers for coherent/incoherent ergotropy contributions. All reported phenomena (non-monotonic ergotropic capacitance, Mpemba crossings under iteration) follow by direct evaluation of these objects as functions of the channel parameters, including temperature. No steps reduce by construction to fitted inputs, self-citations, or imported uniqueness theorems; the chain is self-contained within the introduced definitions and does not rely on external load-bearing premises that collapse to the target claims.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is supplied; no explicit free parameters, background axioms, or invented entities can be extracted from the given text.

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Reference graph

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    Microscopic derivation of the Kraus operators The starting point to associate a general structure to the microscopic model outlined in Fig. 5 is to write the spaces H(E) SB introduced in Eq. (A3). We can divide these subspaces in two categories: 9 1.Non-trivial fixed energy subspaces.In these subspaces the energyEis exactly equal toϵ i fori∈[0, d−1], that...

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