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arxiv: 2605.20166 · v1 · pith:LITYL44Wnew · submitted 2026-05-19 · 🪐 quant-ph · cond-mat.mes-hall· cond-mat.stat-mech

Stochastic trajectories and excursions in a double quantum dot system

Guilherme Fiusa , Pedro E. Harunari , Alberto J. B. Rosal , John M. Nichol , Gabriel T. Landi This is my paper

Pith reviewed 2026-05-20 05:00 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hallcond-mat.stat-mech
keywords stochastic excursionsdouble quantum dotcounting observablesnonequilibrium fluctuationsthermo-kinetic uncertainty relationscharge currentdynamical activityentropy production
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0 comments X

The pith

Stochastic excursions filter double quantum dot trajectories to expose links between currents and excursion times.

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

The paper applies the stochastic excursion framework to the trajectory dynamics of a double quantum dot system. This method divides full trajectories into sub-trajectories, granting direct access to correlations between thermodynamic currents and the durations of those sub-trajectories. For the counting observables of charge current, dynamical activity, and entropy production, the authors derive averages, noise levels, and outcome distributions that illuminate transport trade-offs. State observables are introduced to track dot populations and their correlations. Thermo-kinetic uncertainty relations are used to show how current precision is limited by either entropy production or dynamical activity depending on the regime.

Core claim

Counting observables defined as linear combinations of weighted transition counts within one excursion enable computation of averages and noise for charge current, dynamical activity, and entropy production, while connecting trajectory-level outcome distributions to trade-offs between successful and unsuccessful transport events and bounding precision via thermo-kinetic uncertainty relations.

What carries the argument

Counting observables, defined as linear combinations of transition counts each multiplied by an assigned weight within a single stochastic excursion.

If this is right

  • Averages and fluctuations of charge current, dynamical activity, and entropy production become computable from excursion-filtered data to characterize device operation.
  • Transport outcome distributions directly reflect trade-offs between successful and unsuccessful events that determine overall performance.
  • State observables yield populations of the two dots and their mutual correlations independent of transition counts.
  • Current precision is constrained either by entropy production or by dynamical activity according to the operating regime.

Where Pith is reading between the lines

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

  • The same filtering technique could be applied to other mesoscopic transport setups to expose analogous hidden correlations in their fluctuation statistics.
  • Refinement of the uncertainty relations might yield tighter bounds when additional state information is incorporated.
  • Experimental counting strategies could be redesigned around excursion weights to improve precision for specific observables.

Load-bearing premise

The double quantum dot admits a Markovian jump-process description in which excursions can be defined unambiguously and the chosen weighted transition counts capture the relevant thermodynamic and kinetic correlations.

What would settle it

Measurements in a physical double quantum dot that find no statistical correlation between entropy production and the times of identified excursions would undermine the claimed access to intricate current-time relations.

Figures

Figures reproduced from arXiv: 2605.20166 by Alberto J. B. Rosal, Gabriel T. Landi, Guilherme Fiusa, John M. Nichol, Pedro E. Harunari.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic diagram of the double quantum dot with left and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Sample trajectory in the double quantum dot system, as [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Current and (b) Di [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Current of (a) Dynamical activity [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Probabilities for the transport counting observable within an [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Probabilities for the transport counting observable within an [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Probabilities for the distribution of populations visualized in [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Mutual information between the population of the two dots [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Fano factor for the transport observable as a function of [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Current precision of the transport observable and the three [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. (a) Average of the transport observable [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
read the original abstract

We investigate the trajectory-level dynamics of a double quantum dot system using the newly developed formalism of stochastic excursions. This approach extends full counting statistics by enabling a filtering of complex trajectories into sub-trajectories, which provide access to the intricate correlations between thermodynamic currents and excursion times. Counting observables are the main object of study in the stochastic excursion framework. Those are defined as a linear combination of transition counts multiplied by their assigned weights within one excursion. For three main counting observables -- charge current, dynamical activity, and entropy production -- we compute averages and noise contributions and show how they provide insights into the operation of the double quantum dot system. At the trajectory level, we analyze outcome distributions for transport and connect the results with trade-offs between successful and unsuccessful events that shape overall performance. We further introduce state observables, which depend on the state visited rather than the transition itself, and discuss the population of the two dots, as well as their correlations. Finally, we discuss thermodynamics of precision through thermo-kinetic uncertainty relations, showing how current precision in different regimes is fundamentally constrained either by entropy production or by dynamical activity. Altogether, our work is a case study that highlights the utility of the excursion framework as a toolkit to analyze many quantities of interest and to uncover the structure of nonequilibrium fluctuations. Moreover, it also suggests new avenues for refining uncertainty relations and understanding transport in mesoscopic systems.

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 applies the stochastic excursion formalism to a double quantum dot system, extending full counting statistics by decomposing trajectories into sub-trajectories between reference transitions. It defines counting observables as weighted linear combinations of transition counts and computes their averages, noise, and correlations with excursion times for charge current, dynamical activity, and entropy production. The work also introduces state observables, analyzes transport outcome distributions, and derives thermo-kinetic uncertainty relations that bound current precision by either entropy production or dynamical activity.

Significance. If the central derivations hold, the excursion framework supplies a practical toolkit for dissecting nonequilibrium fluctuations at the trajectory level in mesoscopic systems, yielding concrete trade-offs between successful and unsuccessful transport events and new constraints on precision that complement existing thermodynamic uncertainty relations.

major comments (2)
  1. [Introduction and Sec. II (model definition)] The validity of the entire analysis rests on the assumption that the double quantum dot dynamics are faithfully captured by a continuous-time Markov jump process in which excursions can be defined unambiguously via chosen reference transitions. The manuscript does not provide a quantitative test (e.g., comparison with a coherent or non-Markovian master equation) of the regime in which this approximation remains accurate; if coherent tunneling between dots or memory effects from the leads become appreciable, the reported noise contributions and thermo-kinetic bounds could receive quantum corrections not captured by the jump-process counting observables.
  2. [Sec. V (thermodynamics of precision)] The thermo-kinetic uncertainty relations are presented as fundamental constraints, yet their derivation appears to rely on the same weighted transition counts used for the counting observables. It is unclear whether these relations remain parameter-free or reduce to identities once the weights are chosen to match the physical currents (cf. the definitions of the three main observables).
minor comments (2)
  1. [Figures 2–5] Figure captions should explicitly state the parameter values (bias, temperature, tunneling rates) used for each panel so that the plotted distributions and noise curves can be reproduced without consulting the main text.
  2. [Abstract and Sec. IV] The distinction between counting observables and state observables is introduced late; a brief forward reference in the abstract or introduction would improve readability.

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, providing clarifications and indicating revisions where the manuscript will be updated in the next version.

read point-by-point responses

  1. Referee: [Introduction and Sec. II (model definition)] The validity of the entire analysis rests on the assumption that the double quantum dot dynamics are faithfully captured by a continuous-time Markov jump process in which excursions can be defined unambiguously via chosen reference transitions. The manuscript does not provide a quantitative test (e.g., comparison with a coherent or non-Markovian master equation) of the regime in which this approximation remains accurate; if coherent tunneling between dots or memory effects from the leads become appreciable, the reported noise contributions and thermo-kinetic bounds could receive quantum corrections not captured by the jump-process counting observables.

    Authors: The stochastic excursion formalism is formulated for continuous-time Markov jump processes, which is the standard modeling choice for double quantum dot transport in the incoherent regime where lead-induced decoherence dominates over coherent tunneling. This approximation is widely employed in the literature on mesoscopic charge transport and full counting statistics. We have added a paragraph in the revised introduction that explicitly states the regime of validity, references supporting works on when coherent corrections remain small, and notes that a direct comparison with non-Markovian or coherent master equations lies outside the scope of the present study. revision: partial

  2. Referee: [Sec. V (thermodynamics of precision)] The thermo-kinetic uncertainty relations are presented as fundamental constraints, yet their derivation appears to rely on the same weighted transition counts used for the counting observables. It is unclear whether these relations remain parameter-free or reduce to identities once the weights are chosen to match the physical currents (cf. the definitions of the three main observables).

    Authors: The thermo-kinetic uncertainty relations are obtained from general properties of the excursion decomposition and apply to arbitrary linear combinations of transition counts; they are therefore parameter-free at the level of derivation. When the weights are specialized to the physical observables (charge current, activity, entropy production), the resulting bounds remain non-trivial inequalities that relate precision to either entropy production or dynamical activity. They do not collapse to identities. We have revised Section V to include an expanded derivation that separates the general case from the specific weight choices, making this distinction explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: direct application of excursion framework to DQD trajectories

full rationale

The paper applies the stochastic excursion formalism as an extension of full counting statistics to filter trajectories in a double quantum dot system. Counting observables are explicitly defined as linear combinations of weighted transition counts within excursions, with averages, noise, and correlations computed for charge current, dynamical activity, and entropy production. State observables and thermo-kinetic uncertainty relations are derived from the underlying Markov jump process. No step reduces a reported prediction or central result to a fitted parameter, self-definition, or unverified self-citation chain; the analysis is a case study whose outputs follow from the system's transition rates and excursion definitions without tautological closure. The Markovian assumption is standard for the model and does not create circularity in the derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the applicability of the stochastic excursion formalism to a quantum-dot master equation and on the existence of well-defined excursions; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption The double quantum dot dynamics can be modeled as a continuous-time Markov chain with identifiable transitions.
    Required to define excursions and weighted transition counts.

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