Thermodynamic uncertainty relation in a tilted periodic potential under coarse graining

TL;DR

This paper derives a simplified thermodynamic uncertainty relation (TUR) for particles in a tilted periodic potential using coarse graining, revealing conditions for the TUR bound to increase with affinity.

Contribution

It provides a new coarse-grained derivation of TUR for tilted periodic potentials and analyzes conditions affecting the TUR bound's behavior.

Findings

Derived TUR using transition probabilities in a coarse-grained framework

Identified conditions for the TUR bound to increase monotonically with affinity

Enhanced understanding of TUR behavior in nonequilibrium mesoscopic systems

Abstract

Recently, some general relations have been studied in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a universal internal relation among the cumulants of currents and the entropy production. In this paper, we give a simple derivation of TUR for thermally fluctuating particle current in a tilted periodic potential from a coarse grained point of view with the use of the transition probabilities. Also, we explore the condition for the bound of TUR to monotonically increase with the affinity.