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

Abstract

We study the statistics, in stationary conditions, of the work $W_τ$ 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 $W_τ>W_τ^†$ correspond to configurations where interaction between particles plays a minor role whereas those with $W_τ< W_τ^†$ represent states with single particles dragged by clusters. This two-fold behavior is fully mirrored by the probability distribution $P(W_τ)$ of the work, which does not obey the large-deviation principle for $W_τ<W_τ^†$. 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.

6 pages, 4 figures