Proof of the Finite-Time Thermodynamic Uncertainty Relation for Steady-State Currents

TL;DR

This paper proves a finite-time thermodynamic uncertainty relation for steady-state currents, establishing a universal energetic constraint on current fluctuations over finite observation periods.

Contribution

It provides the first rigorous proof of a finite-time thermodynamic uncertainty relation for steady-state currents, extending previous long-time results.

Findings

Finite-time uncertainty relation is valid for steady-state currents.

The proof uses a quadratic bound on the large deviation rate function.

The relation applies to large ensembles of copies in steady states.

Abstract

The thermodynamic uncertainty relation offers a universal energetic constraint on the relative magnitude of current fluctuations in nonequilibrium steady states. However, it has only been derived for long observation times. Here, we prove a recently conjectured finite-time thermodynamic uncertainty relation for steady-state current fluctuations. Our proof is based on a quadratic bound to the large deviation rate function for currents in the limit of a large ensemble of many copies.