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

Abstract: 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 $W_\tau <sup>\dag$ such that fluctuations with $W_\tau &gt;W_\tau <sup>\dag$ correspond to configurations where interaction between particles plays a minor role whereas those with $W_\tau &lt; W_\tau <sup>\dag$ 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 $W_\tau &lt;W_\tau <sup>\dag$. 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.