# Hyperaccurate currents in stochastic thermodynamics

## TL;DR

This paper introduces the concept of hyperaccurate currents in stochastic thermodynamics, which are the integrated empirical currents with minimal fluctuations, providing improved estimates of entropy production in non-equilibrium systems.

## Contribution

The authors derive a variational principle for hyperaccurate currents in overdamped Langevin systems and analyze their relation to entropy production and thermodynamic uncertainty relations.

## Key findings

- Hyperaccurate current coincides with entropy production when the uncertainty relation is saturated.
- Hyperaccurate currents can significantly reduce fluctuations compared to standard currents.
- The approach improves entropy production estimates from experimental data.

## Abstract

Thermodynamic observables of mesoscopic systems can be expressed as integrated empirical currents. Their fluctuations are bound by thermodynamic uncertainty relations. We introduce the hyperaccurate current as the integrated empirical current with the least fluctuations in a given non-equilibrium system. For steady-state systems described by overdamped Langevin equations, we derive an equation for the hyperaccurate current by means of a variational principle. We show that the hyperaccurate current coincides with the entropy production if and only if the latter saturates the thermodynamic uncertainty relation, and it can be substantially more precise otherwise. The hyperaccurate current can be used to improve estimates of entropy production from experimental data.