Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems

TL;DR

This paper presents a unified framework for analyzing fluctuations in quantum transport using full counting statistics and first-passage times, revealing ensemble relations, effects of metastability, and fluctuation theorems applicable to various quantum systems.

Contribution

It introduces a comprehensive approach connecting full counting statistics and first-passage times in Markovian quantum systems, including new relations and fluctuation theorems.

Findings

Derived ensemble relations linking the two approaches at all times.

Identified violations of cumulant relations due to metastability.

Formulated a fluctuation theorem for first-passage time distributions.

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.