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A hybrid quantum thermodynamic uncertainty relation holds for normal-superconducting conductors with any real superconducting gap.

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Proves a hybrid quantum TUR for N-S conductors valid for arbitrary superconducting gap by showing nonequilibrium excess noise has positive representation in scattering formalism.

T0 review reviewed 2026-06-26 challenge →

load-bearing objection The paper proves a hybrid TUR for NS conductors that holds at arbitrary gap with mixed Andreev-quasiparticle processes by representing excess noise positively.

arxiv 2606.21555 v1 pith:5WIOPS4K submitted 2026-06-19 cond-mat.mes-hall

A thermodynamic uncertainty relation for (hybrid) N--S coherent conductors

Sergi Vidal , Rosa Lopez This is my paper
classification cond-mat.mes-hall
keywords thermodynamic uncertainty relationhybrid normal-superconducting conductorsAndreev reflectionquasiparticle transportnonequilibrium noisesuperconducting gapcharge current fluctuationsentropy production
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper establishes a thermodynamic uncertainty relation that bounds current fluctuations by entropy production in hybrid normal-superconducting systems. It does so by decomposing transport into Andreev, quasiparticle, and interference terms using scattering theory. Although interference complicates additive bounds, the nonequilibrium excess noise can be given a positive representation. This representation enables the proof of the uncertainty relation without restricting the gap value. The result shows how superconducting coherence affects fluctuations while keeping a universal precision-dissipation link.

Core claim

Using the Anantram-Datta scattering formalism, the charge current and zero-frequency noise are decomposed into Andreev, quasiparticle, and interference contributions. The nonequilibrium excess noise admits a positive representation independent of the superconducting gap. This positive representation proves a hybrid quantum thermodynamic uncertainty relation valid for arbitrary real gaps, extending the pure Andreev case to regimes where quasiparticle and Andreev processes coexist.

What carries the argument

The positive representation of the nonequilibrium excess noise derived from the decomposition of current and noise in the Anantram-Datta formalism.

Load-bearing premise

The Anantram-Datta scattering formalism allows decomposition of current and noise such that the nonequilibrium excess noise has a positive representation independent of the gap value.

What would settle it

An observation that the nonequilibrium excess noise takes negative values for some superconducting gap value, or a direct violation of the uncertainty bound in a hybrid conductor with mixed processes.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The manuscript claims to prove a hybrid quantum thermodynamic uncertainty relation (TUR) for normal-superconducting (N-S) coherent conductors. Using the Anantram-Datta scattering formalism, the charge current and zero-frequency noise are decomposed into Andreev, quasiparticle, and interference contributions. The central technical step is showing that the nonequilibrium excess noise admits a positive representation independent of the real superconducting gap Δ; this representation is then used to establish a TUR that extends the pure Andreev case to regimes where quasiparticle and Andreev processes coexist.

Significance. If the positive representation of the excess noise holds without additional assumptions, the result supplies a universal dissipation-precision bound for hybrid quantum conductors. The approach is grounded in standard scattering theory and provides a concrete way to accommodate interference terms while preserving the TUR structure, which is a useful extension beyond the pure Andreev limit.

minor comments (2)
  1. The abstract states that a proof of the positive representation exists, but the manuscript would benefit from an explicit outline or appendix summarizing the key algebraic steps that establish positivity and Δ-independence, to facilitate verification.
  2. Notation for the decomposed currents (Andreev, quasiparticle, interference) should be introduced with a clear table or equation block early in the text for readability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of our manuscript, including the accurate summary of the hybrid quantum TUR and the role of the positive representation of nonequilibrium excess noise. We note the recommendation for minor revision and will incorporate any editorial or typographical suggestions in the revised version.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in scattering formalism

full rationale

The paper decomposes charge current and zero-frequency noise via the standard Anantram-Datta scattering formalism into Andreev, quasiparticle, and interference terms. It then shows that nonequilibrium excess noise (after equilibrium subtraction) admits a positive representation independent of the real gap value Δ. This representation is used to prove the hybrid TUR. No step reduces by construction to a fitted input, self-definition, or load-bearing self-citation; the central claim is a direct consequence of algebraic properties of the scattering decomposition rather than an ansatz or renamed empirical pattern. The argument is therefore self-contained against external benchmarks in mesoscopic transport theory.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the scattering formalism and positive-representation step are treated as background.

reviewed 2026-06-26 · how reviews work

0 comments
Cite this review

Pith. "Pith review of A thermodynamic uncertainty relation for (hybrid) N--S coherent conductors." pith.science (2026). https://pith.science/paper/5WIOPS4K

@misc{pith2026260621555,
  author       = {Pith},
  title        = {Pith review of: A thermodynamic uncertainty relation for (hybrid) N--S coherent conductors},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5WIOPS4K}},
  note         = {Machine review of arXiv:2606.21555}
}
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read the original abstract

Thermodynamic uncertainty relations establish fundamental bounds between current fluctuations and entropy production in nonequilibrium systems. In hybrid normal superconducting conductors, transport is governed by the coexistence of quasiparticle transmission and Andreev reflection, where electron hole conversion transfers charge through the superconducting condensate. Using the Anantram Datta scattering formalism, we decompose the charge current and zero-frequency noise into Andreev, quasiparticle, and interference contributions. Although the interference term prevents a simple additive bound at the level of individual noise components, we show that the nonequilibrium excess noise admits a positive representation. This allows us to prove a hybrid quantum thermodynamic uncertainty relation valid for an arbitrary real superconducting gap. Our result extends the pure Andreev quantum TUR to regimes where quasiparticle and Andreev processes coexist, clarifying how superconducting coherence reshapes current fluctuations while preserving a universal dissipation precision constraint in hybrid quantum conductors.

Figures

Figures reproduced from arXiv: 2606.21555 by Rosa Lopez, Sergi Vidal.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the normal–superconductor hybrid de [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Color maps of the zero-frequency charge noise versus [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Noise versus the applied bias voltage. Zero [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Thermodynamic uncertainty relations, namely, TUR, [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Thermodynamic bound on the Fano factor of a coherent thermoelectric heat engine

    cond-mat.mes-hall 2026-07 accept novelty 6.0

    Heat-engine operation forces a universal Fano-factor floor of F>1/2 for fermionic coherent thermoelectric transport and F>1 for bosonic or classical carriers.

Reference graph

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This paper was first reviewed by grok-4.3 on June 26, 2026.