Large fluctuations and dynamic phase transition in a system of self-propelled particles

We study the statistics, in stationary conditions, of the work $W_\tau$ done by the active force in different systems of self-propelled particles in a time $\tau$. We show the existence of a critical value $W_\tau ^\dag$ such that fluctuations with $W_\tau >W_\tau ^\dag$ correspond to configurations where interaction between particles plays a minor role whereas those with $W_\tau < W_\tau ^\dag$ represent states with single particles dragged by clusters. This two-fold behavior is fully mirrored by the probability distribution $P(W_\tau)$ of the work, which does not obey the large-deviation principle for $W_\tau <W_\tau ^\dag$. This pattern of behavior can be interpreted as due to a phase transition occurring at the level of fluctuating quantities and an order parameter is correspondingly identified.