The role of charge in thermodynamic uncertainty relations

TL;DR

This paper investigates how the charge carried by transport processes affects the validity of thermodynamic uncertainty relations, revealing that higher charge processes can violate existing bounds and proposing a charge-dependent modification.

Contribution

It introduces a charge-dependent quantum TUR and demonstrates its validity and violation conditions in non-interacting electronic transport systems.

Findings

Quantum TUR can be violated by multi-charge transport processes.

A modified quantum TUR incorporating charge is proposed.

Violation occurs only when the highest charge process exceeds the charge-dependent bound.

Abstract

We demonstrate that the charge value of transport mechanisms heavily impacts the validity of thermodynamic uncertainty relations (TURs). Specifically, we show within the framework of full counting statistics, that the recently established quantum TUR can be violated by the presence of transport processes that carry more than one charge, like Andreev reflection processes in normal metal-superconductor junctions. We propose a modified quantum TUR, which incorporates the charge value and demonstrate that this charge-dependent quantum TUR can only be violated if the highest charge transport process exceeds this charge value. In particular, we establish that the breaking of the quantum TUR solely originates from the charge value of the highest charge transport process. Namely, our analytical considerations do not invoke the existence of superconductivity, and these considerations generally hold for non-interacting electronic transport which can be described by the scattering formalism.