Time-resolved Stochastic Dynamics of Quantum Thermal Machines

TL;DR

This paper introduces a framework for analyzing quantum thermal machines at the stochastic cycle level, classifying cycles and assessing operational efficiency through intermittency, with relevance to mesoscopic quantum dot experiments.

Contribution

It presents a novel cycle-based stochastic analysis method for quantum thermal machines, distinguishing cycle types and operational intermittency.

Findings

Classifies quantum thermal machine cycles as engine-like, cooling-like, or idle.

Provides statistical analysis of cycle durations and useful cycle fractions.

Introduces intermittency as a measure of operational consistency.

Abstract

Steady-state quantum thermal machines are typically characterized by a continuous flow of heat between different reservoirs. However, at the level of discrete stochastic realizations, heat flow is unraveled as a series of abrupt quantum jumps, each representing an exchange of finite quanta with the environment. In this work, we present a framework that resolves the dynamics of quantum thermal machines into cycles classified as engine-like, cooling-like, or idle. We analyze the statistics of individual cycle types and their durations, enabling us to determine both the fraction of cycles useful for thermodynamic tasks and the average waiting time between cycles of a given type. Central to our analysis is the notion of intermittency, which captures the operational consistency of the machine by assessing the frequency and distribution of idle cycles. Our framework offers a novel approach to characterizing thermal machines with significant relevance to experiments involving mesoscopic transport through quantum dots.