Large Fluctuations and Dynamic Phase Transition in a System of Self-Propelled Particles

We study the statistics, in stationary conditions, of the work Wτ done by the active force in different systems of self-propelled particles in a time τ. We show the existence of a critical value W†τ such that fluctuations with Wτ > W†τ correspond to configurations where interaction between particles plays a minor role whereas those with Wτ < W†τ represent states with single particles dragged by clusters. This twofold behavior is fully mirrored by the probability distribution P(Wτ) of the work, which does not obey the largedeviation principle for Wτ < W†τ. 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.