Quality of the Thermodynamic Uncertainty Relation for Fast and Slow Driving

TL;DR

This paper investigates the effectiveness of the thermodynamic uncertainty relation under fast and slow driving conditions, identifying observables that optimize entropy production estimates and demonstrating the relation's saturation in certain limits.

Contribution

It analyzes the quality of the thermodynamic uncertainty relation for different observables during fast and slow driving, revealing conditions for optimal entropy estimation and saturation.

Findings

Observables can estimate entropy production with order-one accuracy in both limits.

The thermodynamic uncertainty relation can be saturated under fast driving conditions.

Optimal observables depend on the driving regime and can improve inference accuracy.

Abstract

The thermodynamic uncertainty relation originally proven for systems driven into a non-equilibrium steady state (NESS) allows one to infer the total entropy production rate by observing any current in the system. This kind of inference scheme is especially useful when the system contains hidden degrees of freedom or hidden discrete states, which are not accessible to the experimentalist. A recent generalization of the thermodynamic uncertainty relation to arbitrary time-dependent driving allows one to infer entropy production not only by measuring current-observables but also by observing state variables. A crucial question then is to understand which observable yields the best estimate for the total entropy production. In this paper we address this question by analyzing the quality of the thermodynamic uncertainty relation for various types of observables for the generic limiting cases of fast driving and slow driving. We show that in both cases observables can be found that yield an estimate of order one for the total entropy production. We further show that the uncertainty relation can even be saturated in the limit of fast driving.