Optimal thermodynamic uncertainty relation in Markov jump processes

TL;DR

This paper establishes the optimal form of thermodynamic uncertainty relations in Markov jump processes, identifying the pseudo entropy production as the best Fisher information choice and demonstrating conditions for equality in nonequilibrium systems.

Contribution

It introduces the pseudo entropy production as the optimal Fisher information for TURs and shows how TUR inequalities can be made tight and optimal in certain classes of observables.

Findings

Pseudo entropy production is the optimal Fisher information for TURs.

TUR inequalities become tight and achieve equality with generalized empirical measures.

Hierarchical structure of TUR-type inequalities is established.

Abstract

We investigate the tightness and optimality of thermodynamic-uncertainty-relation (TUR)-type inequalities from two aspects, the choice of the Fisher information and the class of possible observables. We show that there exists the best choice of the Fisher information, given by the pseudo entropy production, and all other TUR-type inequalities in a certain class can be reproduced by this tightest inequality. We also demonstrate that if we observe not only generalized currents but generalized empirical measures, the TUR-type inequality becomes optimal in the sense that it achieves its equality in general nonequilibrium stationary systems. Combining these results, we can draw a hierarchical structure of TUR-type inequalities.