Work fluctuations for a confined Brownian particle: the role of initial conditions

TL;DR

This paper analyzes the large fluctuations of work injected into a confined Brownian particle, revealing how initial conditions influence the singularities in the rate function and identifying big jumps in initial values as the key mechanism.

Contribution

It provides an analytical computation of the rate function for work fluctuations under various initial conditions, highlighting the impact of initial spread and potential strength.

Findings

Rate function exhibits zero, one, or two singularities depending on initial conditions.

Large initial spread and potential strength influence the number of singularities.

Numerical simulations confirm analytical predictions.

Abstract

We study the large fluctuations of the work injected by the random force into a Brownian particle under the action of a confining harmonic potential. In particular, we compute analytically the rate function for generic uncorrelated initial conditions, showing that, depending on the initial spread, it can exhibit no, one, or two singularities associated to the onset of linear tails. A dependence on the potential strength is observed for large initial spreads (entailing two singularities), which is lost for stationary initial conditions (giving one singularity) and concentrated initial values (no singularity). We discuss the mechanism responsible for the singularities of the rate function, identifying it as a big jump in the initial values. Analytical results are corroborated by numerical simulations.