Work fluctuations for a harmonically confined Active Ornstein-Uhlenbeck Particle

TL;DR

This paper analyzes how harmonic confinement affects the fluctuations of active work in an active Ornstein-Uhlenbeck particle, revealing singularities caused by boundary effects and large jumps in trajectories.

Contribution

It provides an analytical study of active work fluctuations under harmonic confinement, highlighting the emergence of singularities and boundary effects in the rate function.

Findings

Harmonic confinement induces singularities in the active work rate function.

Large jumps at trajectory boundaries cause these singularities.

Boundary terms are crucial in understanding the fluctuation behavior.

Abstract

We study the active work fluctuations of an active Ornstein-Uhlenbeck particle in the presence of a confining harmonic potential. We tackle the problem analytically both for stationary and generic uncorrelated initial states. Our results show that harmonic confinement can induce singularities in the active work rate function, with linear stretches at large positive and negative active work, at sufficiently large active and harmonic force constants. These singularities originate from big jumps in the displacement and in the active force, occurring at the initial or ending points of trajectories and marking the relevance of boundary terms in this problem.