Collective motion in large deviations of active particles

TL;DR

This paper investigates how rare large deviation events induce collective motion in active particles, revealing a dynamical phase transition and symmetry breaking through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of collective motion during large deviations in active particles, including an exact solution for two particles and a hydrodynamic theory for many particles.

Findings

Identification of a dynamical phase transition to collective motion.

Exact computation of particle alignment for two particles.

Development of a fluctuating hydrodynamic theory for biased states.

Abstract

We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyse the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state.