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

We study the large deviations of the distribution P(W_\tau) of the work associated with the propulsion of individual active brownian particles in a time interval \tau, in the region of the phase diagram where macroscopic phase separation takes place. P(W_\tau) 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_\tau 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 \tau and the typical persistence times of the particles in the two phases.