Work Fluctuations in the Active Ornstein- Uhlenbeck Particle model

TL;DR

This paper investigates the large deviations of active work in an Active Ornstein-Uhlenbeck Particle model, analyzing free and confined cases, and explores fluctuation relations and the effects of potential types on fluctuation phenomenology.

Contribution

It provides analytical and numerical characterization of the rate function for active work fluctuations in AOUPs, including effects of confinement and potential anharmonicity, and tests fluctuation relations.

Findings

Rate function is asymptotically linear and dimension-independent (except for a factor).

Different fluctuation behaviors for harmonic and anharmonic potentials.

Fluctuation relation holds with a slope related to temperature or effective temperature.

Abstract

We study the large deviations of the power injected by the active force for an Active Ornstein-Uhlenbeck Particle (AOUP), free or in a confining potential. For the free-particle case, we compute the rate function analytically in d-dimensions from a saddle-point expansion, and numerically in two dimensions by it a) direct sampling of the active work in numerical solutions of the AOUP equations and b) Legendre-Fenchel transform of the scaled cumulant generating function obtained via a cloning algorithm. The rate function presents asymptotically linear branches on both sides and it is independent of the system's dimensionality, apart from a multiplicative factor. For the confining potential case, we focus on two-dimensional systems and obtain the rate function numerically using both methods a) and b). We find a different scenario for harmonic and anharmonic potentials: in the former case, the phenomenology of fluctuations is analogous to that of a free particle, but the rate function might be non-analytic; in the latter case the rate functions are analytic, but fluctuations are realised by entirely different means, which rely strongly on the particle-potential interaction. Finally, we check the validity of a fluctuation relation for the active work distribution. In the free-particle case, the relation is satisfied with a slope proportional to the bath temperature. The same slope is found for the harmonic potential, regardless of activity, and for an anharmonic potential with low activity. In the anharmonic case with high activity, instead, we find a different slope which is equal to an effective temperature obtained from the fluctuation-dissipation theorem.