Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir

TL;DR

This paper develops a stochastic thermodynamic framework for a quantum dot coupled to a finite-size reservoir, accounting for reservoir temperature fluctuations and deriving a fluctuation theorem for entropy production.

Contribution

It introduces a novel analysis of heat, work, and entropy production in nano-scale systems with finite reservoirs, filling a gap in existing stochastic thermodynamics.

Findings

Derived a fluctuation theorem for entropy production in finite-reservoir systems.

Demonstrated thermodynamic consistency in the statistical description of the system.

Analyzed work production in a finite-size Szilard engine model.

Abstract

In nano-scale systems coupled to finite-size reservoirs, the reservoir temperature may fluctuate due to heat exchange between the system and the reservoirs. To date, a stochastic thermodynamic analysis of heat, work and entropy production in such systems is however missing. Here we fill this gap by analyzing a single-level quantum dot tunnel coupled to a finite-size electronic reservoir. The system dynamics is described by a Markovian master equation, depending on the fluctuating temperature of the reservoir. Based on a fluctuation theorem, we identify the appropriate entropy production that results in a thermodynamically consistent statistical description. We illustrate our results by analyzing the work production for a finite-size reservoir Szilard engine.