Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems
arXiv:2508.18614 · doi:10.1103/4hc1-l8w4
Abstract
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.
28 pages, 9 figures
References in corpus (89)
- Gaussian Quantum Information
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Shot Noise in Mesoscopic Conductors
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- QuTiP: An open-source Python framework for the dynamics of open quantum systems
- The large deviation approach to statistical mechanics
- Entropy production along a stochastic trajectory and an integral fluctuation theorem
- The physics of exceptional points
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
- Non-Markovian dynamics in open quantum systems
- Microwave photonics with superconducting quantum circuits
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Anomalous transport in the crowded world of biological cells
- Thermodynamic uncertainty relation for biomolecular processes
- A single-atom heat engine
- Dissipation bounds all steady-state current fluctuations
- Dynamical quantum phase transitions: a review
- Quantum jumps of light recording the birth and death of a photon in a cavity
- Real-time quantum feedback prepares and stabilizes photon number states
- Counting statistics of single-electron transport in a quantum dot
- Full Counting Statistics of Charge Transfer in Coulomb Blockade Systems
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
- Experimental demonstration of quantum effects in the operation of microscopic heat engines
- Observing single quantum trajectories of a superconducting qubit
- Experimental characterization of a spin quantum heat engine
- Observation of quantum jumps in a superconducting artificial atom
- Geometry-controlled kinetics
- General non-Markovian dynamics of open quantum systems
- A quantum-dot heat engine operating close to the thermodynamic efficiency limits
- Thermodynamics of Quantum Jump Trajectories
- Quantum feedback: theory, experiments, and applications
- Towards a theory of metastability in open quantum dynamics
- Counting Statistics of Non-Markovian Quantum Stochastic Processes
- {\it Colloquium:} Statistical Mechanics and Thermodynamics at Strong Coupling: Quantum and Classical
- Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
- Mean first-passage times of non-Markovian random walkers in confinement
- A fluctuation theorem for currents and non-linear response coefficients
- Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects
- Analysis of quantum semigroups with GKS--Lindblad generators II. General
- Fundamental Bounds on First Passage Time Fluctuations for Currents
- Current fluctuations in open quantum systems: Bridging the gap between quantum continuous measurements and full counting statistics
- Full counting statistics of nano-electromechanical systems
- Distribution of Entropy Production in a Single-Electron Box
- Stochastic thermodynamics: From principles to the cost of precision
- Decision Making in the Arrow of Time
- Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes
- QuTiP 5: The Quantum Toolbox in Python
- Absorbing state phase transition with competing quantum and classical fluctuations
- Thermodynamics of Precision in Markovian Open Quantum Dynamics
- Observation of quantum jumps of a single quantum dot spin using sub-microsecond single-shot optical readout
- Symmetry and the thermodynamics of currents in open quantum systems
- Thermodynamics of Gambling Demons
- Signatures of Liouvillian exceptional points in a quantum thermal machine
- Optical detection of single electron transport dynamics
- Transport Statistics of Bistable Systems
- Second law of thermodynamics at stopping times
- Quantum contact process
- Signatures of critical full counting statistics in a quantum-dot chain
- Waiting for rare entropic fluctuations
- Theory of classical metastability in open quantum systems
- Fluctuating observation time ensembles in the thermodynamics of trajectories
- Thermodynamic uncertainty relation for first-passage times on Markov chains
- Lee-Yang zeros and large-deviation statistics of a molecular zipper
- Kinetic uncertainty relation on first passage time for accumulated current
- Quantum trajectories and their statistics for remotely entangled quantum bits
- Non-Markovian Quantum Exceptional Points
- First-passage distributions for the one-dimensional Fokker-Planck equation
- Quantum Martingale Theory and Entropy Production
- Reaction-limited quantum reaction-diffusion dynamics
- Unraveling the topology of dissipative quantum systems
- A Cooper-Pair Box Coupled to Two Resonators: An Architecture for a Quantum Refrigerator
- Quantum trajectories of superconducting qubits
- Counting Statistics in Multi-stable Systems
- Counting quantum jumps: a summary and comparison of fixed-time and fluctuating-time statistics in electron transport
- Effect of Measurement Backaction on Quantum Clock Precision Studied with a Superconducting Circuit
- Scaling properties and universality of first-passage time probabilities in financial markets
- First Passage Times for Continuous Quantum Measurement Currents
- Trace of anomalous diffusion in a biased quenched trap model
- Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions
- Quantum jump approach to microscopic heat engines
- Thermodynamic uncertainty relation for quantum first passage process
- Precision is not limited by the second law of thermodynamics
- Topological transitions in quantum jump dynamics: Hidden exceptional points
- Fluctuating-time and full counting statistics for quantum transport in a system with internal telegraphic noise
- Photon counting statistics in Gaussian bosonic networks
- Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents