Steady state fluctuation relations for systems driven by an external random force

TL;DR

This study experimentally investigates work fluctuations in stochastic systems driven by external Gaussian forces, confirming the steady state fluctuation theorem at weak forcing and characterizing deviations at stronger forcing.

Contribution

It provides the first experimental validation of steady state fluctuation relations for systems driven by external Gaussian noise and describes how deviations evolve with forcing amplitude.

Findings

Work fluctuations obey the fluctuation theorem at weak forcing.

Deviations from the fluctuation theorem increase with forcing amplitude.

Deviations collapse onto a master curve depending on the external force type.

Abstract

We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic force microscopy cantilever. We determine the corresponding probability density functions for different random forcing amplitudes ranging from a small fraction to several times the amplitude of the thermal noise. In both systems for sufficiently weak forcing amplitudes the work fluctuations satisfy the usual steady state fluctuation theorem. As the forcing amplitude drives the system far from equilibrium, deviations of the fluctuation theorem increase monotonically. The deviations can be recasted to a single master curve which only depends on the kind of stochastic external force.