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arXiv:2605.20166

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

quant-phcond-mat.mes-hallcond-mat.stat-mechSubmitted May 19, 2026• Announced May 20, 2026• Revised Oct 2, 2026 (v2)
v1 · May 19, 2026v2 · Oct 2, 2026
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Abstract

We investigate the trajectory-level stochastic dynamics of a double quantum dot system using the formalism of stochastic excursions. An excursion is a sub-trajectory that begins when the system leaves a chosen reference state (or more generally, a set of states)---here, the empty double dot---and ends upon its first return to it. Filtering trajectories into excursions extends full counting statistics and gives access to the correlations between thermodynamic currents and excursion durations. The main objects of study are counting observables, defined as weighted sums of transition counts within a single 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 the overall performance of the double quantum dot as a transport device. We then discuss the populations of the two dots, as well as their correlations. Finally, we illustrate how the framework provides insights into the thermodynamics of precision through the Fano factor and thermo-kinetic uncertainty relations, where different regimes are 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.

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We investigate the trajectory-level stochastic dynamics of a double quantum dot system using the formalism of stochastic excursions. An excursion is a sub-trajectory that begins when the system leaves a chosen reference state (or more generally, a set of states)---here, the empty double dot---and ends upon its first return to it. Filtering trajectories into excursions extends full counting statistics and gives access to the correlations between thermodynamic currents and excursion durations. The main objects of study are counting observables, defined as weighted sums of transition counts within a single 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 the overall performance of the double quantum dot as a transport device. We then discuss the populations of the two dots, as well as their correlations. Finally, we illustrate how the framework provides insights into the thermodynamics of precision through the Fano factor and thermo-kinetic uncertainty relations, where different regimes are 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.
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We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum systems governed by Markovian Lindblad dynamics, we derive general ensemble relations that connect the two approaches at all times, and we clarify how the steady states reached at long times relate to those reached at large jump counts. In regimes of metastability, long-lived intermediate states cause violations of experimentally testable cumulant relations, as we discuss. We also formulate a fluctuation theorem governing the probability of rare fluctuations in the first-passage time distributions based on results from full counting statistics. Our results apply to general integer-valued trajectory observables that do not necessarily increase monotonically in time. Three illustrative applications, a two-state emitter, a driven qubit, and a variant of the Su-Schrieffer-Heeger model, highlight the physical implications of our results and provide guidelines for practical calculations. Our framework provides a complete picture of first-passage time statistics in Markovian quantum systems, encompassing multiple earlier results, and it has direct implications for current experiments in quantum optics, superconducting circuits, and nanoscale heat engines.
This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schrödinger equation allows to construct quantum trajectories describing the dynamics of the system state vector in presence of an eventually monitored environment. Thermodynamic quantities are defined at the single quantum trajectory level, independently of any energy measurement, at any time of the protocol. We thereby identify coherent contributions, without classical counterparts, leading to quantum fluctuations of thermodynamic quantities. This formalism eventually leads to central fluctuation theorems for entropy, extending in the quantum regime results obtained in classical stochastic thermodynamics. The thermal imprint of coherences on a simple implementation of Jarzynski equality is investigated, opening avenues for a thermodynamic approach to decoherence.
We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on noninteracting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.
Kinetic uncertainty relations bound current precision of stochastic processes by dynamical activity. The extension of these bounds to quantum systems has been impeded by coherence, strong system-reservoir coupling, and the subtlety of defining dynamical activity in the quantum regime. Here, we introduce a partial dynamical activity through the quantum Fisher information associated with the rescaling of the system-reservoir coupling and show that it bounds current precision via a universal susceptibility-kinetic uncertainty relation. The general validity of this relation for any open quantum system is guaranteed by the natural contribution of a susceptibility term, which is experimentally accessible by tuning the system-reservoir coupling strength. We show how the partial dynamical activity encompasses previous definitions of activity in the weak-coupling Markovian limit and that it provides an information-geometric interpretation of correlator-based activities. We illustrate the tight constraint on precision that our bound provides with the example of steady-state transport through a double quantum dot, where quantum effects invalidate previously developed kinetic uncertainty relations. We expect our bound to provide a powerful tool for optimizing precision in arbitrary quantum systems.
The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.