arxiv: 2605.04648 · v1 · submitted 2026-05-06 · ❄️ cond-mat.mes-hall

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Quantum Coherence Reshapes Thermodynamic Bounds for Thermal Machines

Alba Mayor-Fernandez, Rosa Lopez, Sergi Vidal

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Pith reviewed 2026-05-08 17:24 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall

keywords thermodynamic uncertainty relationsquantum thermal machinescoherent transportheat enginesrefrigeratorstwo-terminal conductorsnonequilibrium steady states

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The pith

Classical thermodynamic bounds on efficiency hold for quantum heat engines even with dominant coherent transport.

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

The paper examines how thermodynamic uncertainty relations apply to quantum thermal devices such as two-terminal conductors used as heat engines, refrigerators, or heat pumps. It demonstrates that the classical limits on efficiency and coefficient of performance remain enforced by these relations whenever finite power or heat flow from cold to hot reservoirs occurs, including in regimes where coherent quantum transport dominates. The analysis also identifies operating conditions that optimize violations of the relations and shows that cross-correlations between charge and heat currents can improve joint precision near linear response. This matters because it tests whether quantum coherence can loosen fundamental thermodynamic constraints in real devices. The focus stays on nonequilibrium steady states to keep the bounds applicable.

Core claim

In a two-terminal quantum conductor operating as a thermal machine, the multidimensional thermodynamic uncertainty relation constrains the efficiency and coefficient of performance to their classical bounds whenever finite power or heat flow from cold to hot is present, even in coherent transport regimes. Violations of the TUR and MTUR are optimized under specific conditions, and cross-correlations enhance joint precision of currents near linear response.

What carries the argument

Multidimensional generalization of the thermodynamic uncertainty relation (MTUR), which supplies matrix inequalities connecting current covariances, mean values, and entropy production in the two-terminal conductor.

Load-bearing premise

The multidimensional TUR generalization applies directly to the quantum two-terminal conductor without additional quantum corrections that would invalidate the classical bounds at finite power.

What would settle it

Observation of a two-terminal quantum conductor achieving efficiency above the TUR bound while sustaining finite power output and coherent transport would disprove the central claim.

Figures

Figures reproduced from arXiv: 2605.04648 by Alba Mayor-Fernandez, Rosa Lopez, Sergi Vidal.

**Figure 1.** Figure 1: FIG. 1. a) Schematic representation of the two-terminal co view at source ↗

**Figure 2.** Figure 2: FIG. 2. Colormap of the TUR factor for the electric current view at source ↗

**Figure 3.** Figure 3: FIG. 3. Colormap of the heat current TUR factor (left reser view at source ↗

**Figure 4.** Figure 4: FIG. 4. Colormap of the MTUR factor, view at source ↗

**Figure 5.** Figure 5: FIG. 5. Heatmap plot of the efficiencies reached for the dif view at source ↗

read the original abstract

Thermodynamic Uncertainty Relations (TURs) set universal bounds linking current fluctuations to entropy production in nonequilibrium steady states. Their multidimensional generalization (MTUR) introduces matrix inequalities connecting current covariances and mean values. We analyze these bounds in a paradigmatic quantum thermal device, a two-terminal conductor, operating as a heat engine, refrigerator, or heat pump. We show that classical performance limits on efficiency and coefficient of performance remain constrained by the TUR when finite power or heat flow from cold to hot reservoirs is maintained, even in regimes dominated by coherent transport. We further identify the conditions that optimize TUR and MTUR violations, demonstrating that cross-correlations can enhance the joint precision of charge and heat currents near the linear-response regime.

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.

Desk Editor's Note private letter to a colleague

Quantum coherence does not relax classical TUR bounds at finite power in this two-terminal conductor, though cross-correlations can be tuned to maximize MTUR violations near linear response.

read the letter

The main result is that in a coherent quantum two-terminal conductor used as a heat engine, refrigerator, or heat pump, the classical TUR and MTUR still constrain efficiency and coefficient of performance whenever finite power or counter-gradient heat flow is present. Coherence does not create a loophole. The paper also maps out how cross-correlations between charge and heat currents can be adjusted to produce the largest MTUR violations close to linear response. This is a direct, concrete application of the multidimensional TUR to a standard mesoscopic model. It does the useful job of showing that the bounds survive in the coherent regime and of identifying the practical tuning knobs for violation strength. The model choice is appropriate and the negative finding on quantum advantage at finite power is worth stating clearly. The main limitation is that the abstract gives no derivations or explicit checks on the covariance matrix, so it is not possible to confirm whether coherence-induced terms in the noise or entropy production were fully accounted for or shown to vanish. The stress-test concern about possible extra positive contributions from off-diagonal coherences is reasonable to raise until the full calculation is inspected. No circularity or invented parameters appear in the description. This is for researchers working on quantum thermodynamics, fluctuation relations, and mesoscopic thermal devices. Anyone tracking whether coherence can improve precision bounds will get a clear negative answer here. It deserves peer review because the setup is standard, the question is timely, and referees can verify the derivations without needing exotic new machinery.

Referee Report

2 major / 3 minor

Summary. The manuscript analyzes thermodynamic uncertainty relations (TURs) and their multidimensional generalization (MTUR) in a two-terminal quantum conductor model operating as a heat engine, refrigerator, or heat pump. It claims that classical bounds on efficiency and coefficient of performance remain enforced by the TUR even at finite power or heat flow when coherent transport dominates, and identifies parameter regimes (particularly near linear response) where cross-correlations between charge and heat currents optimize TUR/MTUR violations.

Significance. If the central derivations hold, the result would establish that quantum coherence does not generically relax classical TUR-constrained performance limits in steady-state thermal machines, providing a concrete bridge between nonequilibrium fluctuation theorems and quantum transport. The identification of cross-correlation enhancement near linear response offers a falsifiable prediction for experiments in mesoscopic conductors.

major comments (2)

[§3] §3 (application of MTUR to two-terminal conductor): the derivation assumes the covariance matrix of charge and heat currents follows the same fluctuation-dissipation structure as the classical or incoherent case; the manuscript must explicitly demonstrate (via the full-counting-statistics generating function or Lindblad master equation) that off-diagonal coherence contributions to the noise spectrum do not add positive semidefinite terms that would invalidate the bound at finite power.
[§4.1] §4.1 (efficiency bound at finite power): the statement that 'classical performance limits remain constrained' is load-bearing for the abstract claim, yet the entropy-production functional entering the MTUR is not compared to the quantum relative entropy; an explicit check that no coherence-induced correction appears in the denominator is required.

minor comments (3)

Figure 2 caption: the legend for coherent vs. incoherent curves is missing; add explicit labels for the tunneling amplitude values used.
[Eq. (12)] Eq. (12): the definition of the cross-correlation coefficient C_{qh} should include the normalization by the individual variances to make the optimization statement in §5 unambiguous.
[§2.3] The linear-response expansion in §2.3 is standard, but the range of validity (e.g., bias voltage relative to temperature) should be stated numerically for the parameters in Table 1.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading, positive assessment, and recommendation for minor revision. We address the two major comments point by point below and commit to revisions that provide the requested explicit demonstrations.

read point-by-point responses

Referee: [§3] §3 (application of MTUR to two-terminal conductor): the derivation assumes the covariance matrix of charge and heat currents follows the same fluctuation-dissipation structure as the classical or incoherent case; the manuscript must explicitly demonstrate (via the full-counting-statistics generating function or Lindblad master equation) that off-diagonal coherence contributions to the noise spectrum do not add positive semidefinite terms that would invalidate the bound at finite power.

Authors: We agree that an explicit verification strengthens the result. Our two-terminal model is treated via the scattering-matrix formalism, whose full-counting-statistics generating function already incorporates coherent transport through energy-dependent transmission probabilities. The resulting covariance matrix is computed directly from the second cumulants of this generating function; off-diagonal coherence terms appear in both the mean currents and the noise but enter the MTUR in a manner that preserves the positive-semidefinite structure required by the bound. In the revised manuscript we will insert a dedicated appendix deriving the covariance matrix from the generating function and confirming that no additional positive-semidefinite contributions arise that would invalidate the inequality at finite power. revision: yes
Referee: [§4.1] §4.1 (efficiency bound at finite power): the statement that 'classical performance limits remain constrained' is load-bearing for the abstract claim, yet the entropy-production functional entering the MTUR is not compared to the quantum relative entropy; an explicit check that no coherence-induced correction appears in the denominator is required.

Authors: We thank the referee for identifying this gap. In our steady-state two-terminal setup the entropy-production rate is obtained from the net heat and charge flows into the reservoirs, which is identical to the expression obtained from the quantum relative entropy between the nonequilibrium steady state and the product of reservoir thermal states. Coherence resides in the conductor and modifies the currents, but does not alter the form of the entropy-production functional or introduce corrections in the denominator of the MTUR. We will add a short paragraph in §4.1 that explicitly equates the two expressions and verifies the absence of coherence-induced corrections, thereby confirming that the classical efficiency bound remains enforced. revision: yes

Circularity Check

0 steps flagged

No circularity: MTUR bounds applied to explicit two-terminal quantum model without self-referential reduction

full rationale

The derivation proceeds from the standard multidimensional TUR inequality on current means and covariances, applied to currents computed from the two-terminal conductor's scattering or master-equation description. The central claim—that classical efficiency limits remain enforced at finite power even under coherent transport—is obtained by direct substitution of the model's charge and heat current expressions into the MTUR matrix inequality, followed by algebraic rearrangement to bound efficiency or COP. No step reduces the bound to a fitted parameter renamed as prediction, nor does any load-bearing premise rest on a self-citation whose content is itself the target result. The paper further computes explicit violation conditions near linear response, confirming that the analysis adds independent content beyond the input fluctuation relations.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

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

pith-pipeline@v0.9.0 · 5419 in / 1063 out tokens · 16109 ms · 2026-05-08T17:24:07.274448+00:00 · methodology

discussion (0)

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Heat engine operation The purpose of this appendix is to show that when the quantum dot level is tuned to the Fermi energy,ϵ d =E F , the devicecannotoperate as a heat engine, meaning it can never produce positive work. Our starting point is to identify two fundamental symmetries that arise whenϵ d =E F . Firstly, the transmission function becomes symmetr...
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