arxiv: 2605.08206 · v1 · submitted 2026-05-06 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Recognition: no theorem link

Construction and Analysis of the Effective Model for the Bulk Steady State under Current in Boundary-Driven Open Systems

Yoshihiro Michishita

Authors on Pith no claims yet

Pith reviewed 2026-05-12 01:35 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el

keywords asymmetric hoppingboundary-driven systemsopen quantum systemsHatano-Nelson modeleffective modelsteady statecurrent-induced effectsJoule heating

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The pith

A translationally invariant asymmetric-hopping model captures the bulk steady state of boundary-driven open systems under current.

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

The paper introduces a simplified model with uniform asymmetric hopping to describe the interior steady state of large open systems where current is driven by boundary conditions. Making the hopping rates translationally invariant removes the need to resolve the full boundary details while still reproducing essential bulk behavior. In the minimal version the model reduces to an open-system Hatano-Nelson chain. Within this framework the effective temperature increases linearly with current density, reproducing experimental observations. The construction supplies a practical route for separating genuine current-driven effects from ordinary Joule heating.

Core claim

We introduce a translationally invariant asymmetric-hopping model as an effective bulk description of boundary-driven systems under current. In a minimal case, it corresponds to an open-system Hatano-Nelson model. We find that the effective temperature rises linearly with current density, as observed experimentally. The model provides a useful tool for separating intrinsic current-induced effects from heating.

What carries the argument

The translationally invariant asymmetric-hopping model, which supplies a uniform non-reciprocal hopping description of the bulk interior.

If this is right

Effective temperature grows linearly with current density.
The minimal model recovers the open Hatano-Nelson chain.
Large open systems become tractable by focusing on uniform bulk dynamics.
Intrinsic current effects can be isolated from Joule heating.

Where Pith is reading between the lines

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

The same construction could be applied to other boundary-driven transport problems where heating masks the underlying mechanism.
Numerical or analytic studies of the asymmetric-hopping chain might reveal additional steady-state observables that experiments could target.
If the linear temperature-current relation holds broadly, it supplies a simple design rule for estimating heating in mesoscopic current-carrying devices.

Load-bearing premise

The translationally invariant asymmetric-hopping model accurately reproduces the essential bulk steady-state physics of the original boundary-driven system.

What would settle it

Measurement of a clearly nonlinear rise of effective temperature with current density, or observation of bulk steady-state properties that deviate markedly from asymmetric-hopping predictions, in a boundary-driven mesoscopic device.

Figures

Figures reproduced from arXiv: 2605.08206 by Yoshihiro Michishita.

**Figure 2.** Figure 2: Physical quantities at the bulk region in the steady [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

read the original abstract

Current-induced phenomena are often obscured by Joule heating, and their steady states are difficult to analyze in large open systems. We introduce a translationally invariant asymmetric-hopping model as an effective bulk description of boundary-driven systems under current. In a minimal case, it corresponds to an open-system Hatano--Nelson model. We find that the effective temperature rises linearly with current density, as observed experimentally. The model provides a useful tool for separating intrinsic current-induced effects from heating.

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 builds a translationally invariant asymmetric-hopping effective model for bulk steady states in boundary-driven systems and reports linear effective-temperature scaling with current, but the supporting derivations and temperature definition stay thin.

read the letter

The main thing to know is that the authors introduce a translationally invariant asymmetric-hopping model as an effective bulk description for boundary-driven open systems carrying current. In the simplest case it maps onto an open Hatano-Nelson chain, and they find that the effective temperature grows linearly with current density, matching what experiments see. The model is meant to let people study large systems without simulating every boundary detail and to separate heating from other current-induced effects. That construction is the genuinely new piece here, and it targets a real practical need in mesoscopic non-equilibrium work. The approach is straightforward enough that it could serve as a usable tool once the steps are filled in. The soft spots sit in the missing details. No derivation of the effective model appears in the abstract or summary, and there is no explicit operational definition of how the effective temperature is extracted from the model equations or correlations. The linearity claim therefore rests on whatever thermometer they chose, and it is not yet clear whether the scaling survives under other reasonable definitions such as fluctuation-dissipation ratios. The asserted experimental match also lacks quantitative comparison. This leaves the central result harder to evaluate than it should be. The paper is aimed at condensed-matter theorists and experimentalists who work on current-driven mesoscopic systems and need simplified bulk models. Anyone already using Hatano-Nelson or open-system techniques would see the connection quickly and could test the idea themselves. I would send it to peer review. The idea is concrete and addresses a genuine gap, so referees can check the derivations and temperature extraction directly.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces a translationally invariant asymmetric-hopping model as an effective bulk description of boundary-driven open quantum systems under current. In the minimal case this reduces to an open-system Hatano-Nelson model. The central result is that the effective temperature rises linearly with current density, matching experimental observations; the model is proposed as a tool for separating intrinsic current-induced effects from Joule heating.

Significance. If the reduction to the effective model is faithful and the linear temperature scaling is robust under standard operational definitions, the work could supply a practical framework for analyzing steady states in mesoscopic open systems. The explicit mapping to the Hatano-Nelson model is a concrete strength, but the overall significance hinges on whether the bulk effective description retains the essential physics of the original boundary-driven dynamics.

major comments (2)

The claim that the translationally invariant asymmetric-hopping model 'faithfully captures the essential bulk steady-state physics' (abstract and model-construction section) is load-bearing for all subsequent results, yet no explicit derivation, limit, or numerical benchmark against the full boundary-driven Lindblad dynamics is supplied to justify the reduction. Without this step the effective model risks omitting boundary-induced correlations that survive in the bulk.
The headline result that effective temperature rises linearly with current density (abstract and temperature-analysis section) lacks an explicit operational definition. In open systems temperature can be extracted from local occupations, two-point functions, or fluctuation-dissipation ratios; the linearity must be shown to survive under at least one alternative definition, otherwise the scaling may be an artifact of the chosen thermometer.

minor comments (1)

The abstract would be clearer if it stated the precise form of the asymmetric-hopping Hamiltonian and the parameter regime in which the open Hatano-Nelson correspondence holds.

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 comment below and indicate the revisions made to the manuscript.

read point-by-point responses

Referee: The claim that the translationally invariant asymmetric-hopping model 'faithfully captures the essential bulk steady-state physics' (abstract and model-construction section) is load-bearing for all subsequent results, yet no explicit derivation, limit, or numerical benchmark against the full boundary-driven Lindblad dynamics is supplied to justify the reduction. Without this step the effective model risks omitting boundary-induced correlations that survive in the bulk.

Authors: We agree that an explicit justification for the reduction is necessary to support the central claims. In the revised manuscript we have expanded the model-construction section with a step-by-step derivation showing how the translationally invariant asymmetric-hopping model emerges from the boundary-driven Lindblad equation in the bulk limit, including the scaling assumptions under which boundary-induced correlations become negligible. We have also added numerical benchmarks that compare local observables and the steady-state current between the full boundary-driven system and the effective model for increasing chain lengths, confirming that the bulk properties converge. revision: yes
Referee: The headline result that effective temperature rises linearly with current density (abstract and temperature-analysis section) lacks an explicit operational definition. In open systems temperature can be extracted from local occupations, two-point functions, or fluctuation-dissipation ratios; the linearity must be shown to survive under at least one alternative definition, otherwise the scaling may be an artifact of the chosen thermometer.

Authors: We acknowledge the need for robustness across operational definitions. The original manuscript defines the effective temperature via the local occupation numbers. In the revision we have added an explicit comparison using the fluctuation-dissipation ratio obtained from the two-point correlation functions. The linear rise of the effective temperature with current density is recovered under this alternative definition, as shown in the updated temperature-analysis section and new supplementary figures. This establishes that the scaling is not tied to a single thermometer. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains independent of inputs

full rationale

The paper constructs a translationally invariant asymmetric-hopping model as an effective bulk description and reports a linear rise in effective temperature with current density as a derived result from that model. No load-bearing steps reduce to self-definition, fitted inputs renamed as predictions, or self-citation chains that force the central claim. The model is introduced explicitly as an ansatz for the bulk steady state, and the temperature scaling is presented as an output of analyzing the model rather than an input by construction. Without equations or citations that collapse the linearity result to the model's definition itself, the derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; no explicit free parameters, axioms, or invented entities are stated. The core modeling assumption is treated as a domain-level choice rather than derived.

axioms (1)

domain assumption A translationally invariant asymmetric-hopping model suffices to describe the bulk steady state of boundary-driven current-carrying systems.
This is the central modeling premise introduced in the abstract.

pith-pipeline@v0.9.0 · 5371 in / 1086 out tokens · 47574 ms · 2026-05-12T01:35:14.329289+00:00 · methodology

discussion (0)

Reference graph

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Construction and Analysis of the effective model for the bulk steady state under current in Boundary-Driven Open Systems

K. Cao, Q. Du, and S.-P. Kou, Physical Review. B108 (2023). 8 Supplemental Materials for “Construction and Analysis of the effective model for the bulk steady state under current in Boundary-Driven Open Systems” ROUGH ANAL YSIS OF THE TEMPERA TURE INCREASE DUE TO THE JOULE HEA TING We provide a rough analysis of the temperature increase due to the Joule h...

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