Dissipated work and fluctuation relations for non-equilibrium single-electron transitions

TL;DR

This paper investigates fluctuation relations in a single-electron box, demonstrating that while the Jarzynski equality is approximately valid under overheating conditions, an entropy-based relation remains accurate, supported by simulations.

Contribution

The study provides analytical and numerical evidence that the integral fluctuation relation based on entropy production holds in overheated single-electron systems, extending fluctuation relation applicability.

Findings

Jarzynski equality is approximately valid with overheated electrons.

An entropy-based fluctuation relation remains valid in overheated conditions.

Monte Carlo simulations agree with theoretical predictions.

Abstract

We discuss a simple but experimentally realistic model system, a single-electron box (SEB), where common fluctuation relations can be tested for driven electronic transitions. We show analytically that when the electron system on the SEB island is overheated by the control parameter (gate voltage) drive, the common fluctuation relation (Jarzynski equality) is only approximately valid due to dissipated heat even when the system starts at thermal equilibrium and returns to it after the drive has been stopped. However, an integral fluctuation relation based on total entropy production works also in this situation. We perform extensive Monte Carlo simulations of single-electron transitions in the SEB setup and find good agreement with the theoretical predictions.