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arxiv: 2604.10322 · v2 · submitted 2026-04-11 · ❄️ cond-mat.mes-hall · cond-mat.stat-mech· quant-ph

Stochastic entropy production in scattering theory

Ludovico Tesser , Henning Kirchberg , Matteo Acciai , Janine Splettstoesser This is my paper

Pith reviewed 2026-05-10 15:14 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.stat-mechquant-ph
keywords stochastic entropy productionscattering theorycoherent transportstochastic thermodynamicsLandauer-Büttiker formulastwo-point measuremententropy currentsfluctuations
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The pith

A stochastic description of entropy production in scattering theory separates information entropy from thermodynamic entropy.

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

The paper develops a stochastic framework for entropy production inside scattering theory for coherent transport. It separates the information entropy change arising from incomplete knowledge of the leads' state from the thermodynamic entropy change that occurs when each lead equilibrates with its bath. A two-point measurement scheme tracks the stochastic entropy production at successive stages and supplies the full statistics of transport quantities. Restricted to ordinary particle or energy currents the method recovers the Landauer-Büttiker formulas. The same construction extends immediately to entropy currents and their fluctuations, thereby linking stochastic thermodynamics to coherent scattering.

Core claim

We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change due to the equilibration of each lead with its bath. By employing a two-point measurement scheme, we access the stochastic entropy production at these different stages of the process, as well as the statistics of generic transport quantities. When restricted to particle or energy transport, our approach reproduces the Landauer-Büttiker formulas. The possibility to consider more general quantities such as the entropy currents and their fluctuations, provid

What carries the argument

The two-point measurement scheme applied to scattering processes, which records stochastic changes separately in information entropy and thermodynamic entropy.

If this is right

  • The approach reproduces the Landauer-Büttiker formulas for particle and energy transport.
  • It supplies the statistics of generic transport quantities including entropy currents.
  • It establishes a direct link between stochastic thermodynamics and coherent transport through entropy fluctuations.

Where Pith is reading between the lines

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

  • The framework could be applied to more complex mesoscopic structures such as quantum dots or interferometers.
  • Experiments in quantum transport might measure entropy-production distributions directly.
  • The separation of entropy types may clarify the role of information in fluctuation theorems for coherent systems.

Load-bearing premise

The leads remain in thermal equilibrium with their baths, scattering stays fully coherent, and the two-point measurement can be realized without back-action that would mix information and thermodynamic entropy.

What would settle it

An experiment that measures the full distribution of entropy production in a coherent scattering device and finds statistics that deviate from the predictions of the two-point measurement scheme.

Figures

Figures reproduced from arXiv: 2604.10322 by Henning Kirchberg, Janine Splettstoesser, Ludovico Tesser, Matteo Acciai.

Figure 1
Figure 1. Figure 1: (a) Schematic representation of the process considered. The input state [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

We formulate a stochastic description of entropy production in scattering theory for coherent transport. We distinguish between the information entropy change due to partial knowledge of the leads' state and the thermodynamic entropy change due to the equilibration of each lead with its bath. By employing a two-point measurement scheme, we access the stochastic entropy production at these different stages of the process, as well as the statistics of generic transport quantities. When restricted to particle or energy transport, our approach reproduces the Landauer-B\"uttiker formulas. The possibility to consider more general quantities such as the entropy currents and their fluctuations, provides a systematic connection between stochastic thermodynamics and coherent transport.

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 manuscript formulates a stochastic description of entropy production in scattering theory for coherent transport. It distinguishes the information entropy change (due to partial knowledge of the leads' states) from the thermodynamic entropy change (due to equilibration of each lead with its bath). Using a two-point measurement scheme, the approach accesses stochastic entropy production at different stages and the statistics of generic transport quantities. When restricted to particle or energy transport, it reproduces the Landauer-Büttiker formulas for averages; the framework also allows consideration of entropy currents and their fluctuations, providing a systematic link between stochastic thermodynamics and coherent transport.

Significance. If the two-point measurement construction is shown to preserve coherence and cleanly separate the entropy contributions without back-action, the result would offer a useful bridge between stochastic thermodynamics and mesoscopic coherent transport. This could enable systematic study of fluctuations in entropy production and currents beyond the standard average Landauer-Büttiker expressions, with potential applications to fluctuation theorems in quantum transport setups.

major comments (2)
  1. [formulation of the two-point measurement scheme] The central construction relies on a two-point measurement scheme applied to the leads' states before and after scattering. The manuscript must provide an explicit demonstration (with the relevant density-matrix evolution or Kraus operators) that this scheme introduces no back-action capable of decohering the scattering process or mixing information entropy with thermodynamic entropy. Without this, the claim that the stochastic description applies specifically to coherent transport remains unverified, as the separation of the two entropy types is load-bearing for the entire framework.
  2. [reproduction of Landauer-Büttiker formulas and entropy-current statistics] The reproduction of Landauer-Büttiker formulas is stated for averages when restricted to particle or energy transport. The manuscript should derive the stochastic entropy production explicitly (including the expression for the entropy current fluctuations) and show step-by-step how the average reduces to the known Landauer-Büttiker result without additional fitting parameters or post-hoc choices. This is necessary to confirm that higher-order statistics remain consistent with the coherent-transport assumptions.
minor comments (2)
  1. [notation and definitions] Clarify the notation for the information entropy versus thermodynamic entropy in the main equations; the distinction is conceptually important but the symbols could be made more distinct to avoid reader confusion.
  2. [introduction] Add a brief discussion or reference to prior work on two-point measurements in quantum transport to situate the assumptions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and have revised the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: The central construction relies on a two-point measurement scheme applied to the leads' states before and after scattering. The manuscript must provide an explicit demonstration (with the relevant density-matrix evolution or Kraus operators) that this scheme introduces no back-action capable of decohering the scattering process or mixing information entropy with thermodynamic entropy. Without this, the claim that the stochastic description applies specifically to coherent transport remains unverified, as the separation of the two entropy types is load-bearing for the entire framework.

    Authors: We agree that an explicit demonstration is necessary to rigorously establish the absence of back-action. In the revised manuscript we have added a new subsection (II.C) containing the requested derivation. We consider the composite density matrix of the leads and scattering region, apply the unitary scattering operator, and construct the two-point projective measurements on the lead states via the corresponding Kraus operators. These operators act exclusively on the lead degrees of freedom and commute with the scattering unitary in the coherent-transport limit, leaving the off-diagonal coherences in the scattering region unaffected. The information-entropy contribution is isolated as the change in the von Neumann entropy of the measured lead states, while the thermodynamic contribution arises solely from the subsequent bath equilibration; the two remain additively separate with no cross terms generated by the measurement. This explicit construction confirms that the framework applies to coherent transport without introducing decoherence or mixing the entropy types. revision: yes

  2. Referee: The reproduction of Landauer-Büttiker formulas is stated for averages when restricted to particle or energy transport. The manuscript should derive the stochastic entropy production explicitly (including the expression for the entropy current fluctuations) and show step-by-step how the average reduces to the known Landauer-Büttiker result without additional fitting parameters or post-hoc choices. This is necessary to confirm that higher-order statistics remain consistent with the coherent-transport assumptions.

    Authors: We thank the referee for this request. The revised manuscript now contains an explicit, step-by-step derivation in Section III and Appendix B. Starting from the joint probability distribution of the two-point measurements on particle (or energy) number in the leads, we define the stochastic entropy production as the sum of the information term (log-ratio of forward and reverse probabilities) and the thermodynamic term (chemical-potential or temperature difference times the transferred quantity). Averaging over all trajectories yields exactly the Landauer-Büttiker expression for the mean entropy-production rate (heat current divided by temperature) with no adjustable parameters or additional assumptions. We further compute the second moment of the entropy current and verify that its fluctuations are consistent with the coherent-transport fluctuation theorems, again without post-hoc choices. These derivations confirm that both averages and higher-order statistics remain within the coherent-transport framework. revision: yes

Circularity Check

0 steps flagged

No circularity: formulation connects stochastic thermodynamics to scattering theory via independent two-point measurement scheme

full rationale

The paper formulates a stochastic description distinguishing information entropy (from partial lead-state knowledge) and thermodynamic entropy (from bath equilibration) using a two-point measurement scheme on leads. When restricted to particle or energy currents it recovers the standard Landauer-Büttiker averages, showing consistency with external results rather than tautological reproduction. No equation reduces a claimed prediction to a fitted input by construction, no self-citation chain bears the central premise, and no ansatz or uniqueness theorem is smuggled in via prior author work. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard domain assumptions of coherent scattering and thermal baths; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Transport occurs via coherent scattering between leads that remain in thermal equilibrium with their baths
    Stated as the setting for the stochastic description.

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