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 $W_{\tau }^{†}$ such that fluctuations with $W_{\tau }>W_{\tau }^{†}$ correspond to configurations where interaction between particles plays a minor role whereas those with $W_{\tau }<W_{\tau }^{†}$ 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 $W_{\tau }<W_{\tau }^{†}$. 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

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