Work fluctuations of self-propelled particles in the phase separated state

We study the large deviations of the distribution P(W τ ) of the work associated with the propulsion of individual active Brownian particles in a time interval τ, in the region of the phase diagram where macroscopic phase separation takes place. P(W τ ) is characterised by two peaks, associated to particles in the gaseous and in the clusterised phases, and two separate non-convex branches. Accordingly, the generating function of W τ 's cumulants displays a double singularity. We discuss the origin of such non-convex branches in terms of the peculiar dynamics of the system phases, and the relation between the observation time τ and the typical persistence times of the particles in the two phases