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.

Long-time position distribution of an active Brownian particle in two dimensions

“…While this rate function Φ x (z) was found to be related to the lowest eigenvalue of the Mathieu equation via a Legendre transform, the asymptotic behaviors of Φ x (z) were not extracted. Interestingly, the same rate function Φ x (z) was also found in the current distribution of an interacting active particle system [37], within an effective mean-field description, that just renormalises the single particle velocity v 0 which now depends on the density ρ -still, the asymptotic properties of Φ x (z) were not analysed. In this paper, we show that, for z ∈ [0, 1], the rate function Φ(z) in Eq.…”

Dissipation bounds the amplification of transition rates far from equilibrium

“…Active Brownian particles provide a canonical realization of how autonomous athermal noise can drive novel steady states without simply imparting an effective temperature (17). These self-propelled agents exhibit dynamical symmetry breaking and collective motion (18,19), and previous studies have shown that the escape of active particles from a metastable potential exhibits interesting behavior arising from an interplay between the driving force, persistence time statistics, and the shape of the potential (20,21). For simplicity, we take a symmetric potential, with lA = lB = 1 and β∆VA = β∆VB = 10, setting γ = 1 and kBT = 1/2.…”

Dissipation controls transport and phase transitions in active fluids: mobility, diffusion and biased ensembles

“…The auxiliary dynamics considered previously are for exclusion processes [84][85][86][87], particle-based diffusive systems restricted to small noise regimes [88,89] and non-interacting cases in specific potentials [90][91][92]. Interestingly, recent works have also put forward explicit solutions in active systems for a mean-field dynamics [93] and for a many-body dynamics with pair-wise forces [36].…”