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arxiv: 2604.17152 · v1 · submitted 2026-04-18 · 🪐 quant-ph

Recognition: unknown

Thermodynamics of Coherence-Selective Quantum Reset Protocols

Jishad Kumar , Achilleas Lazarides , Tapio Ala-Nissila
Authors on Pith no claims yet

Pith reviewed 2026-05-10 06:20 UTC · model grok-4.3

classification 🪐 quant-ph
keywords coherence-selective resetquantum thermodynamicsstroboscopic mapopen quantum systemsheat currentfermionic bathcoherence preservationquadratic systems
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The pith

Quantum reset protocols retain maximum coherence at a different point than maximum heat dissipation.

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

This paper develops an exact theory of coherence-selective stroboscopic resetting for quadratic open quantum systems using the single-particle density-matrix formalism. It introduces a one-parameter family of reset channels that interpolates continuously between complete coherence erasure and complete coherence preservation. For a single fermionic level coupled to a structured semi-infinite tight-binding bath, the authors derive the exact affine stroboscopic map, locate its unique fixed point, and compute the retained coherence spectrum, post-reset occupation, and reset heat current. Retained coherence increases monotonically with the retention parameter, but the reset heat current is generically nonmonotonic and reaches its maximum at an intermediate operating point. The work supplies exact operating diagrams and shows that the same coherence-cost tradeoff persists at nonzero chemical potential as a filling-biased deformation rather than a separate particle-current optimization.

Core claim

We introduce a one-parameter family of reset channels that continuously interpolates between complete coherence erasure and complete coherence preservation. For a single fermionic level coupled to a structured semi-infinite tight-binding bath, we derive the exact affine stroboscopic map, solve for its unique fixed point, and compute the retained coherence spectrum, the post-reset occupation, and the reset heat current. We find that retained coherence increases monotonically with the retention parameter, whereas the reset heat current is generically nonmonotonic and is maximized at an intermediate operating point. Thus the protocol that stores the most coherence is not the one that dissipates

What carries the argument

A one-parameter family of reset channels interpolating between complete coherence erasure and complete coherence preservation, realized through an affine stroboscopic map whose unique fixed point yields the retained coherence and reset heat current.

Load-bearing premise

The open quantum system must be quadratic so that it can be treated exactly within the single-particle density-matrix formalism, yielding an affine stroboscopic map with a unique fixed point.

What would settle it

Measure the reset heat current versus the retention parameter in a single fermionic level coupled to a tight-binding bath and check whether the current reaches its maximum at an intermediate retention value rather than at the coherence-preserving endpoint.

Figures

Figures reproduced from arXiv: 2604.17152 by Achilleas Lazarides, Jishad Kumar, Tapio Ala-Nissila.

Figure 1
Figure 1. Figure 1: FIG. 1. Exact baseline thermodynamic comparison for the [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Exact fixed-point retained-coherence spectra [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Exact fixed- [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Exact fixed-point landscapes for the coherence-selective reset channel in the [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Exact Pareto-style operating diagrams in the [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the resulting µ-sweep line cuts at fixed τ J = 0.2 for four representative values of η. The upper row corresponds to the inside-band level ω0/J = 0.8, while the lower row corresponds to the outside-band level ω0/J = 3.0. Several clear conclusions emerge. First, both C ∗ SE and J ∗ Q are strongly nonmonotonic as functions of µ. Second, the maxima are displaced to positive µ, and this displacement beco… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Exact operating-point extraction. Top row: maximizing values of [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
read the original abstract

We develop an exact theory of coherence-selective stroboscopic resetting for quadratic open quantum systems within the single-particle density-matrix formalism. We focus on the survival of coherences and the associated thermodynamic cost at the stroboscopic fixed point. To this end, we introduce a one-parameter family of reset channels that continuously interpolates between complete coherence erasure and complete coherence preservation. This unifies the reset-map description, the repeated-interaction and evolving-correlation endpoint channels, and the thermodynamic cost of environmental reinitialization. For a single fermionic level coupled to a structured semi-infinite tight-binding bath, we derive the exact affine stroboscopic map, solve for its unique fixed point, and compute the retained coherence spectrum, the post-reset occupation, and the reset heat current. We find that retained coherence increases monotonically with the retention parameter, whereas the reset heat current is generically nonmonotonic and is maximized at an intermediate operating point. Thus the protocol that stores the most coherence is not the one that dissipates the most heat. Exact operating diagrams further show that coherence-optimal and coherence-per-cost-optimal protocols are both driven toward the coherence-preserving endpoint, while the heat-optimal protocol depends strongly on the reset interval. We also show that this coherence-cost geometry survives at nonzero chemical potential as a filling-biased deformation of the same fixed-point tradeoff, rather than as an independent particle-current optimization problem. These results establish coherence-selective resetting as a distinct control principle for structured-bath open quantum systems and provide an exactly solvable benchmark for memory engineering and thermodynamic optimization under repeated environmental reinitialization.

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

1 major / 4 minor

Summary. The manuscript develops an exact theory of coherence-selective stroboscopic resetting for quadratic open quantum systems in the single-particle density-matrix formalism. It introduces a one-parameter family of reset channels interpolating between full coherence erasure and preservation, derives the affine stroboscopic map for a single fermionic level coupled to a semi-infinite tight-binding bath, solves for the unique fixed point, and computes the retained coherence spectrum, post-reset occupation, and reset heat current. The central results are that retained coherence increases monotonically with the retention parameter while the reset heat current is generically nonmonotonic (maximized at an intermediate point), so that the most coherence-preserving protocol is not the one with highest heat dissipation; optimal-protocol diagrams and the persistence of the tradeoff at nonzero chemical potential are also reported.

Significance. If the derivations hold, the work supplies an exactly solvable benchmark for thermodynamic optimization under repeated environmental reinitialization in structured baths. The unification of reset-map, repeated-interaction, and evolving-correlation channels within a single parameterized family, together with the closed-form fixed-point analysis and parameter-free construction, constitutes a clear strength; the reported monotonicity/non-monotonicity geometry and the coherence-per-cost operating diagrams provide falsifiable predictions for memory engineering applications.

major comments (1)
  1. [§5] §5, after Eq. (28): the claim that the heat current is 'generically nonmonotonic' rests on numerical sampling of the fixed-point expressions over a range of reset intervals; an analytical demonstration that the derivative with respect to the retention parameter changes sign for arbitrary bath parameters would make the generality statement rigorous rather than observational.
minor comments (4)
  1. [Abstract] Abstract and §3: the term 'exact operating diagrams' is used without specifying whether the diagrams are obtained from closed-form expressions or from numerical root-finding of the fixed-point equations.
  2. [Eq. (15)] Eq. (15): the definition of the retained coherence spectrum should explicitly state its normalization and its relation to the off-diagonal elements of the single-particle density matrix.
  3. [Figure 4] Figure 4: the color bar for the coherence-per-cost quantity lacks units and the contour lines are difficult to read at the high-retention end; adding a second panel with line cuts would improve clarity.
  4. [§2.2] §2.2: several foundational references on repeated-interaction schemes and stroboscopic maps for open fermionic systems are missing from the bibliography.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation and the constructive comment on our manuscript. We respond to the major comment point by point below.

read point-by-point responses

  1. Referee: [§5] §5, after Eq. (28): the claim that the heat current is 'generically nonmonotonic' rests on numerical sampling of the fixed-point expressions over a range of reset intervals; an analytical demonstration that the derivative with respect to the retention parameter changes sign for arbitrary bath parameters would make the generality statement rigorous rather than observational.

    Authors: We thank the referee for this observation. The fixed-point expressions for occupation, retained coherence, and heat current are closed-form but involve nontrivial integrals over the bath spectral density that depend on the retention parameter. This structure makes a general analytical proof that the derivative with respect to the retention parameter changes sign for completely arbitrary bath parameters and reset intervals technically involved. We have confirmed the non-monotonicity through extensive numerical sampling over wide ranges of bandwidths, reset intervals, and chemical potentials. In the revised manuscript we will (i) explicitly qualify the 'generically nonmonotonic' statement as being supported by comprehensive numerical evidence and (ii) add an analytical demonstration of sign change in the derivative for the wide-band limit, where the expressions reduce to algebraic forms whose derivative can be shown to change sign. This constitutes a partial revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained exact solution

full rationale

The paper derives the affine stroboscopic map directly from the quadratic Hamiltonian and the one-parameter family of reset channels within the single-particle density-matrix formalism for the specified fermionic model. It then solves for the unique fixed point of this map and computes retained coherence, occupation, and heat current as direct consequences of that fixed-point solution. The reported monotonic increase in retained coherence with the retention parameter and the non-monotonic heat current follow as numerical properties of the closed-form expressions without any parameter fitting, self-referential definitions, or load-bearing self-citations. The uniqueness of the fixed point is a standard property of affine maps in this context and is not imported via author-specific theorems. No ansatz is smuggled in via citation, and no known result is merely renamed. The central claims are therefore independent of the inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that the system is quadratic (allowing single-particle treatment) and on the newly introduced one-parameter reset-channel family; no additional free parameters or invented entities are evident from the abstract.

free parameters (1)
  • retention parameter
    Continuous interpolation parameter between complete coherence erasure and complete preservation; its value is varied to map the operating diagrams.
axioms (2)
  • domain assumption Quadratic open quantum systems admit an exact single-particle density-matrix description.
    Invoked to derive the affine stroboscopic map and its fixed point.
  • domain assumption Stroboscopic resetting reaches a unique fixed point whose properties determine retained coherence and reset heat current.
    Used to compute the reported spectra and currents.

pith-pipeline@v0.9.0 · 5585 in / 1539 out tokens · 62240 ms · 2026-05-10T06:20:41.656782+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

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    Retained coherence and coherence spectrum The exact post-reset fixed-point SPDM has the block form ρfp = Pfp xfp yfp C0 ,(C1) where the row vectorxfp contains all system–environment coherences after the reset. In the bath eigenbasis ofMEE, its components are xfp k =⟨0|ρ fp|k⟩.(C2) Because each mode carries a distinct coherence ampli- tude, the most micros...

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    Exact pre-reset bath block To derive the heat current, we first need the exact pre- reset bath SPDM. Starting from the exact fixed-point post-reset stateρ fp, one cycle of unitary evolution gives ρ− fp =U(τ)ρ fpU †(τ).(C7) From the block multiplication derived in Appendix A, the bottom-right block is C − fp =wP fpw† +Xy fpw† +wx fpX † +XC 0X †.(C8) Each t...

  3. [3]

    Thus the exact pre-reset bath SPDM depends not only on the system occupation but also explicitly on the retained coherence block

    wPfpw† is the bath population generated directly from the occupied system level during the unitary segment; 2.X yfpw† andwx fpX † are the two terms linear in the retained coherence; 3.XC 0X † is the dressed propagation of the reference bath block through the unitary segment. Thus the exact pre-reset bath SPDM depends not only on the system occupation but ...

  4. [4]

    The energy removed from the bath by that reset step is therefore Q∗ sup(τ, η) = TrE MEE(C − fp −C 0) ,(C9) which is Eq.(56)

    Reset heat and heat current The reset operation restores the bath block fromC − fp to C0. The energy removed from the bath by that reset step is therefore Q∗ sup(τ, η) = TrE MEE(C − fp −C 0) ,(C9) which is Eq.(56). The corresponding heat current per cycle is obtained by dividing by the cycle length, J ∗ Q(τ, η) = Q∗ sup(τ, η) τ .(C10) This is Eq.(57). Bec...

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    Its role is to quantify how much retained coherence is obtained per unit reset-heat cost

    Coherence efficiency and operating points The coherence-efficiency ratio is defined by R∗(τ, η) = C∗ SE(τ, η) J ∗ Q(τ, η) .(C18) This quantity has no independent microscopic derivation: it is a composite operational figure of merit built from the exact retained coherence and exact reset heat current. Its role is to quantify how much retained coherence is ...

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