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arxiv: 2606.13500 · v1 · pith:VMO3OKWNnew · submitted 2026-06-11 · ❄️ cond-mat.mes-hall · cond-mat.stat-mech

Thermoelectric information engine driven by an autonomous Maxwell demon across quantum-to-classical transitions

Maximiliano Bernal Santiba\~nez , Felipe Barra , Jose Mondaca This is my paper

Pith reviewed 2026-06-27 05:45 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.stat-mech
keywords thermoelectric information engineautonomous Maxwell demonquantum coherencephonon-induced decoherencequantum-to-classical transitioninformation flowRedfield master equationdouble quantum dot
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The pith

Phonon-induced decoherence suppresses both coherent transport and information flow to the monitoring dot in a parameter region of this thermoelectric engine, indicating coherence can enhance the autonomous Maxwell demon mechanism.

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

This paper examines a three-terminal thermoelectric engine in which a double quantum dot connects two reservoirs at different chemical potentials and a third dot monitors occupation through Coulomb interaction to act as an autonomous Maxwell demon. Dynamics are described by a Redfield master equation that reveals two steady-state regimes captured by distinct Lindblad approximations, separated by a quantum-to-classical transition controlled by interdot tunneling strength. Introduction of a phonon bath coupled to the double dot generates a second transition through incoherent transport and decoherence. In a specific parameter region the phonon-induced effects reduce both the coherent contribution to transport and the information flow toward the monitoring dot. The analysis shows how coherent tunneling, decoherence, and phonon-assisted transport compete while identifying the appropriate thermodynamic Lindblad description for each regime.

Core claim

Within the parameter range where the device operates as an engine, phonon-induced decoherence suppresses both the coherent transport contribution and the information flow toward the monitoring dot. This occurs across two quantum-to-classical transitions, the first controlled by interdot tunneling strength and the second by the phonon bath, with the Redfield master equation identifying distinct dynamical regimes whose steady states are well captured by suitable Lindblad approximations. The model demonstrates competition among coherent tunneling, decoherence, and incoherent phonon-assisted transport in an autonomous information engine and clarifies which thermodynamic Lindblad description appl

What carries the argument

The autonomous Maxwell demon realized by the third monitoring dot coupled via Coulomb interaction to the double-dot system; it provides information-based feedback that drives the engine, with the Redfield master equation tracking the two quantum-to-classical transitions and the associated changes in coherent versus incoherent transport and information flow.

If this is right

  • The device functions as an engine only in parameter ranges where the demon interpretation holds.
  • Two distinct dynamical regimes exist, each with its own valid Lindblad approximation for the steady state.
  • The phonon bath induces a second quantum-to-classical transition that generates incoherent transport.
  • Coherence enhances the demon mechanism inside the identified parameter region.
  • Tracking information and transport properties across the crossovers determines the correct thermodynamic Lindblad description for each regime.

Where Pith is reading between the lines

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

  • If phonon decoherence suppresses information flow, then engineering reduced phonon coupling in similar quantum-dot devices could extend the range where the demon mechanism operates efficiently.
  • The competition between coherent tunneling and phonon-assisted transport suggests that analogous autonomous information engines in other platforms may exhibit performance gains when coherence is preserved.
  • The two transitions provide a concrete map for tuning between quantum and classical operation that could be tested by varying tunneling strength and phonon bath temperature independently.
  • The finding that coherence can enhance the demon points to possible design rules for maximizing information-to-work conversion in mesoscopic thermoelectric systems.

Load-bearing premise

The Redfield master equation accurately captures the full dynamics and the two Lindblad approximations remain valid in their respective steady-state regimes.

What would settle it

Measurement of the information flow to the monitoring dot in the small interdot tunneling regime with phonon coupling, showing that the flow does not decrease as phonon strength increases while coherent transport is suppressed.

Figures

Figures reproduced from arXiv: 2606.13500 by Felipe Barra, Jose Mondaca, Maximiliano Bernal Santiba\~nez.

Figure 1
Figure 1. Figure 1: FIG. 1. Scheme of the system composed of three quan [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Coherence in the eigen basis [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Energy flow, Power, contribution of information, [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Coherence [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Absolute value of the particle current [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Plot of the ratio [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Plot of the particle current [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

We study a three-terminal thermoelectric engine, focusing on the role of quantum coherence and information flow. A double-dot connects two reservoirs at different chemical potentials, while a third dot monitors their occupation via Coulomb interaction and can be interpreted as an autonomous Maxwell demon. Within the parameter range where the device operates as an engine, we identify conditions under which this interpretation holds. The system dynamics is described within a Redfield master equation that allows us to identify two distinct dynamical regimes with steady states well captured by suitable Lindblad approximations. These two regimes define a first quantum-to-classical transition controlled by the interdot tunneling strength. We further consider the effect of a phonon bath coupled to the double-dot, which induces a second quantum-to-classical transition by generating incoherent transport and decoherence in the small interdot tunneling regime. We identify a parameter region where phonon-induced decoherence suppresses both the coherent transport contribution and the information flow toward the monitoring dot, suggesting that coherence can enhance the demon mechanism in this regime. By tracking information and transport properties across these crossovers, our model shows how coherent tunneling, decoherence, and incoherent phonon-assisted transport compete in an autonomous information engine, while clarifying which thermodynamic Lindblad description is appropriate in each 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.

Referee Report

2 major / 2 minor

Summary. The manuscript models a three-terminal thermoelectric information engine in which a double quantum dot, coupled to two fermionic reservoirs, is monitored by a third dot via Coulomb interaction that functions as an autonomous Maxwell demon. Dynamics are treated with a Redfield master equation that identifies two dynamical regimes whose steady states are captured by distinct Lindblad approximations; these regimes define a tunneling-controlled quantum-to-classical transition and a second transition induced by a phonon bath. In a specific parameter window the phonon bath is reported to suppress both coherent transport and information flow to the monitor, leading to the claim that coherence can enhance the demon mechanism.

Significance. If the central claims hold, the work supplies a concrete example of how coherent tunneling, phonon-assisted incoherent transport, and information flow compete in an autonomous information engine and clarifies which Lindblad form is thermodynamically appropriate in each regime. The explicit tracking of information-theoretic quantities across both crossovers is a useful contribution to the mesoscopic thermodynamics literature.

major comments (2)
  1. [§4] §4 (phonon-bath section) and the associated Redfield generator: the reported suppression of information flow to the monitoring dot is obtained from the steady-state solution of the Redfield equation in the small-tunneling regime once the phonon bath is added. Because Redfield is second-order perturbative in all system-bath couplings, the secular/Markov assumptions can fail precisely when the double-dot is simultaneously coupled to two fermionic reservoirs and the bosonic bath; a concrete check (positivity of the generator or local detailed balance) is needed in the window that defines the second quantum-to-classical crossover.
  2. [Eqs. (Lindblad matching)] Eqs. defining the two Lindblad approximations (around the first and second transitions): the matching of Redfield steady states to the Lindblad forms is used to interpret the demon mechanism, yet the manuscript does not quantify the error between the Redfield and Lindblad currents or information flows in the crossover region itself; without this error estimate the claim that coherence enhances the demon mechanism rests on an unverified extrapolation.
minor comments (2)
  1. Notation for the information-flow term is introduced without an explicit reference to the underlying formula (e.g., the expression for the mutual information rate); a one-line reminder of the definition would improve readability.
  2. Figure captions for the phonon-bath scans should state the fixed values of all other parameters (Γ, U, T, etc.) so that the plotted curves can be reproduced without consulting the main text.

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 the two major points below.

read point-by-point responses

  1. Referee: [§4] §4 (phonon-bath section) and the associated Redfield generator: the reported suppression of information flow to the monitoring dot is obtained from the steady-state solution of the Redfield equation in the small-tunneling regime once the phonon bath is added. Because Redfield is second-order perturbative in all system-bath couplings, the secular/Markov assumptions can fail precisely when the double-dot is simultaneously coupled to two fermionic reservoirs and the bosonic bath; a concrete check (positivity of the generator or local detailed balance) is needed in the window that defines the second quantum-to-classical crossover.

    Authors: We thank the referee for this important observation on the validity of the Redfield approach with multiple baths. In the parameter window defining the phonon-induced crossover, all system-bath couplings remain weak and our internal checks confirm that the generator stays positive and satisfies local detailed balance to high accuracy. We will add an explicit verification of these properties (including a short discussion and, if space permits, a supplementary plot) to the revised manuscript. revision: yes

  2. Referee: [Eqs. (Lindblad matching)] Eqs. defining the two Lindblad approximations (around the first and second transitions): the matching of Redfield steady states to the Lindblad forms is used to interpret the demon mechanism, yet the manuscript does not quantify the error between the Redfield and Lindblad currents or information flows in the crossover region itself; without this error estimate the claim that coherence enhances the demon mechanism rests on an unverified extrapolation.

    Authors: We agree that an explicit error estimate between Redfield and Lindblad predictions in the crossover would strengthen the presentation. The central claim that coherence enhances the demon mechanism is drawn from the Redfield steady-state currents and information flows themselves; the Lindblad forms are used only to interpret the mechanism inside the two well-defined regimes. Nevertheless, we will add a quantitative comparison of the relative deviations in currents and information flows as functions of tunneling and phonon coupling, thereby delineating the validity range of each approximation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses standard master-equation methods without self-referential reduction

full rationale

The paper solves the Redfield master equation for the three-terminal system, matches its steady states to two Lindblad forms to delineate quantum-to-classical regimes, and tracks information flow and transport across phonon-induced decoherence. No step defines a quantity in terms of itself, renames a fitted parameter as a prediction, or relies on a self-citation chain for the central coherence-enhancement claim. The thermodynamic interpretations follow directly from the solved equations under stated approximations, making the derivation self-contained against external benchmarks rather than circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The Redfield equation and Lindblad forms are standard tools, not new postulates.

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discussion (0)

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Reference graph

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    The negativity of ˙F2 observed in Fig

    Thus, the energetic contribution to ˙F2 is positive. The negativity of ˙F2 observed in Fig. 3(a) is therefore entirely due to the information termT ˙I2 <0. Figure 3(b) shows the corresponding thermodynamic quantities associated with subsystem a = 1, namely the monitoring dotD. Since particles do not tunnel be- tweenDand the working substance, ˙W1 = 0 and ...

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    Explicit expressions for the phonon bath The phonon-bath system coupling Eq. (2) features the single bath operator ˆBph =P k(hkˆbk +h ∗ kˆb† k), which cou- ples to the system operator ˆS= ˆd† R ˆdL + ˆd† L ˆdR. This system operator satisfies ˆS=e i ˆHS t ˆSe−i ˆHS t, therefore, we find that the only relevant Bohr frequency isω= 0, see Eq. B3, and that the...

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    Explicit expressions for the fermionic baths In the expression for the coupling with the fermionic reservoirB j (withj∈ {L, R, D}), Eq. (3), the corre- sponding operators ˆBj,l=± are ˆBj,+ = P λ tj,λˆcλ and ˆBj,− =P λ tj,λˆc† λ. Replacing ˆBj± in Eq.(B2) and taking the real part we obtain the decay rates γ(Bj ) + (ϵ) =κ j(ϵ)fj(ϵ), γ (Bj ) − (ϵ) =κ j(ϵ)(1−...

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