# Finite-time generalization of the thermodynamic uncertainty relation

## TL;DR

This paper extends the thermodynamic uncertainty relation to finite timescales, enabling its application to single-molecule experiments and providing potentially tighter bounds on entropy production.

## Contribution

It generalizes the thermodynamic uncertainty relation to finite-time fluctuations, broadening its applicability beyond long-time limits.

## Key findings

- Finite-time relation holds for arbitrary fluctuation timescales.
- Finite-time bounds can be stronger than long-time bounds.
- Application demonstrated with laser tweezer experiments.

## Abstract

For fluctuating currents in non-equilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving. We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales. This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite timescales are not accessible. Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit. We illustrate the relation for the fluctuating work that is performed by a stochastically switching laser tweezer on a trapped colloidal particle.