Current fluctuations of interacting active Brownian particles

Abstract

We derive the distribution of particle currents for a system of interacting active Brownian particles in the long-time limit using large deviation theory and a weighted many-body expansion. We find the distribution is non-Gaussian, except in the limit of passive particles. The non-Gaussian fluctuations can be understood from the effective potential the particles experience when conditioned on a given current. This potential suppresses fluctuations of the particles orientations and surrounding density, aligning particles and reducing their effective drag. From the distribution of currents, we compute the diffusion coefficient, which is in excellent agreement with molecular dynamics simulations over a range of self-propulsion velocities and densities. We show that mass transport is Fickian in that the diffusion constant determines the response of a small density gradient, and that nonlinear responses are similarly computable from the density dependence of the current distribution.