Tight uncertainty relations for cycle currents

TL;DR

This paper derives tighter bounds on the precision of cycle currents in thermodynamic systems, linking them to affinities and improving upon previous dissipation-based inequalities, with implications for non-equilibrium analysis.

Contribution

It introduces novel uncertainty relations specifically for cycle currents, enhancing the understanding of thermodynamic precision bounds beyond transition-based measures.

Findings

Cycle current bounds are stricter than previous dissipation-based inequalities.

The new bounds remain valid far from equilibrium.

Application to a simple model demonstrates improved precision constraints.

Abstract

Several recent inequalities bound the precision of a current - counting net number of transitions in a system - by a thermodynamic measure of dissipation. However, while currents may be defined locally, dissipation is a global property. Inspired by the fact that ever since Carnot cycles are the unit elements of thermodynamic processes, we prove similar bounds tailored to cycle currents - counting net cycle completions - in terms of their conjugate affinities. We show that these inequalities are stricter than previous ones, even far from equilibrium, and that they allow to tighten those on transition currents. We illustrate our results with a simple model and discuss some technical and conceptual issues related to shifting attention from transition to cycle observables.