Connection between the GKSL master equation and the Landauer formula

Misa Nozaki; Takatoshi Fujita

arxiv: 2606.27132 · v1 · pith:6VXXLF7Tnew · submitted 2026-06-25 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

Connection between the GKSL master equation and the Landauer formula

Misa Nozaki , Takatoshi Fujita This is my paper

Pith reviewed 2026-06-26 03:23 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall

keywords GKSL master equationLandauer formulaquantum transportopen quantum systemscurrent formulanon-interacting systemsmesoscopic physics

0 comments

The pith

GKSL master equation yields a current formula that reduces to the Landauer formula for non-interacting systems under specific conditions.

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

The paper derives an expression for electric current from the Gorini-Kossakowski-Sudarshan-Lindblad master equation when the system contains no particle interactions. It then isolates the conditions on the baths and couplings that make this expression identical to the Landauer formula. A sympathetic reader cares because both formalisms are used to compute steady-state transport through small quantum conductors; showing their agreement in the non-interacting case supplies a concrete bridge between the master-equation and scattering-theory descriptions. The work therefore clarifies when results obtained in one language can be trusted in the other without additional corrections.

Core claim

Within the GKSL master equation formalism applied to a non-interacting system, a current formula is obtained that coincides exactly with the Landauer formula once the system satisfies the stated conditions on the reservoir couplings and steady-state populations.

What carries the argument

Derivation of the current formula directly from the GKSL master equation for a non-interacting system, which permits term-by-term comparison with the Landauer expression.

If this is right

The Landauer formula can be recovered as a limiting case inside the GKSL framework without additional assumptions.
Currents in non-interacting open systems can be computed equivalently by either method when the stated conditions hold.
The equivalence supplies a consistency check for numerical implementations of the GKSL equation in transport problems.

Where Pith is reading between the lines

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

The identified conditions may serve as a benchmark when extending the GKSL approach to weakly interacting systems where Landauer is not directly available.
The connection suggests that master-equation methods could be used for device geometries that are awkward for scattering theory.
It opens the possibility of systematic comparison between the two formalisms in exactly solvable models.

Load-bearing premise

The system must be non-interacting so that the master-equation current can be compared directly to the Landauer formula.

What would settle it

A concrete calculation or measurement in which the GKSL-derived current differs from the Landauer result for a demonstrably non-interacting system under the identified conditions would falsify the claimed reduction.

Figures

Figures reproduced from arXiv: 2606.27132 by Misa Nozaki, Takatoshi Fujita.

read the original abstract

We derive a current formula within the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation formalism for a non-interacting system, and identify the conditions under which it reduces to the Landauer formula.

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

The paper derives an explicit current formula from the GKSL master equation for non-interacting systems and states the conditions for reduction to the Landauer formula.

read the letter

The central result is a derivation of a steady-state current expression inside the GKSL formalism for a non-interacting system, plus the limits where that expression collapses to the usual Landauer formula. This is the concrete thing the work supplies.

The derivation itself is the new piece. GKSL is the standard Markovian master equation, and Landauer is the scattering approach for coherent transport; showing the explicit mapping and the required conditions (non-interacting particles, appropriate weak-coupling or Markovian limits) gives a direct bridge between the two. That link can be handy for people who start from open-system equations and want to recover the familiar current formula without switching formalisms.

The paper does this cleanly on its own terms. The non-interacting assumption is stated up front, which matches the regime where Landauer applies, so there is no obvious mismatch. The stress-test note finds no internal inconsistency in the stated claim, and nothing in the abstract suggests parameter fitting or circular steps.

The main limitation is that only the abstract is visible here, so the actual algebra and any intermediate approximations cannot be checked. If the reduction requires extra steps that are not fully justified or if the current formula contains hidden assumptions beyond non-interacting, that would need to be verified in the full text. Otherwise the scope is modest and the claim is proportionate.

This is for readers working on mesoscopic transport or open quantum systems who already use GKSL equations. A specialist who needs the explicit connection would find it useful. It is worth sending to peer review so referees can inspect the derivation steps and confirm the reduction conditions hold as stated.

Referee Report

0 major / 1 minor

Summary. The manuscript derives a current formula within the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation formalism applied to a non-interacting system and identifies the conditions under which the derived expression reduces to the Landauer formula.

Significance. If the derivation holds, the work supplies an explicit mapping between the GKSL open-system approach and the Landauer scattering formula in the non-interacting regime. This is a useful clarification for quantum transport theory, as both formalisms are known to apply there; the paper's contribution lies in exhibiting the precise limits and the resulting current expression rather than in new physics.

minor comments (1)

The abstract is terse; a brief statement of the system Hamiltonian or the form of the GKSL dissipator in the main text would help readers immediately locate the non-interacting assumption.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. The report contains no major comments requiring a point-by-point response.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper states it derives a current formula inside the GKSL master equation for an explicitly non-interacting system and identifies the conditions for reduction to the Landauer formula. Both formalisms are independently known to apply in the non-interacting regime, so the task reduces to exhibiting an explicit mapping under stated limits. No self-citations, fitted parameters renamed as predictions, self-definitional steps, or ansatz smuggling are described in the provided abstract or reader summary. The derivation chain is therefore self-contained against external benchmarks and receives the default non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5554 in / 985 out tokens · 35443 ms · 2026-06-26T03:23:43.889703+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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2025

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Datta,Electronic Transport in Mesoscopic Systems(Cam- bridge University Press, 1995)

S. Datta,Electronic Transport in Mesoscopic Systems(Cam- bridge University Press, 1995)

1995

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Meir and N

Y . Meir and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett.68, 2512 (1992)

1992

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Harbola, M

U. Harbola, M. Esposito, and S. Mukamel, Quantum master equation for electron transport through quantum dots and single molecules, Phys. Rev. B74, 235309 (2006)

2006

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Timm, Tunneling through molecules and quantum dots: Master-equation approaches, Phys

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J. E. Subotnik, T. Hansen, M. A. Ratner, and A. Nitzan, Nonequilibrium steady state transport via the reduced density matrix operator, The Journal of Chemical Physics130, 144105 (2009)

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