Role of Hidden Slow Degrees of Freedom in the Fluctuation Theorem

TL;DR

This paper investigates how hidden slow degrees of freedom affect the fluctuation theorem in a coupled colloidal system, revealing deviations from expected symmetry and highlighting the importance of accessible degrees of freedom.

Contribution

It experimentally examines the impact of hidden slow degrees of freedom on the fluctuation theorem, providing theoretical and experimental insights into apparent entropy production.

Findings

Apparent entropy production obeys a fluctuation theorem-like symmetry with slope 1 at short times.

At longer times, the slope deviates from 1, indicating hidden degrees of freedom influence.

Intermediate nonlinear behavior can be observed by tuning experimental parameters.

Abstract

The validity of the fluctuation theorem for entropy production as deduced from the observation of trajectories implicitly requires that all slow degrees of freedom are accessible. We experimentally investigate the role of hidden slow degrees of freedom in a system of two magnetically coupled driven colloidal particles. The apparent entropy production based on the observation of just one particle obeys a fluctuation theorem-like symmetry with a slope of 1 in the short time limit. For longer times, we find a constant slope, but different from 1. We present theoretical arguments for a generic linear behavior both for small and large apparent entropy production but not necessarily throughout. By fine-tuning experimental parameters, such an intermediate nonlinear behavior can indeed be recovered in our system as well.