Fluctuation theorems for capacitively coupled electronic currents

TL;DR

This paper investigates fluctuation theorems in a system of two capacitively coupled quantum dots, revealing conditions under which single-current fluctuation theorems hold and characterizing back-action effects.

Contribution

It demonstrates the validity of single-current fluctuation theorems in specific limits and introduces an effective affinity concept influenced by back-action effects.

Findings

Single-current fluctuation theorem holds at large Coulomb repulsion.

The theorem also holds at high current ratios between channels.

An effective affinity lower than reservoir affinity is identified and characterized.

Abstract

The counting statistics of electron transport is theoretically studied in a system with two capacitively coupled parallel transport channels. Each channel is composed of a quantum dot connected by tunneling to two reservoirs. The nonequilibrium steady state of the system is controlled by two affinities or thermodynamic forces, each one determined by the two reservoirs of each channel. The status of a single-current fluctuation theorem is investigated starting from the fundamental two-current fluctuation theorem, which is a consequence of microreversibility. We show that the single-current fluctuation theorem holds in the limit of a large Coulomb repulsion between the two parallel quantum dots, as well as in the limit of a large current ratio between the parallel channels. In this latter limit, the symmetry relation of the single-current fluctuation theorem is satisfied with respect to an effective affinity that is much lower than the affinity determined by the reservoirs. This back-action effect is quantitatively characterized.