Mechanical analysis of a dynamical phase transition for particles in a channel

Abstract

We analyze biased ensembles of trajectories for a two-dimensional system of particles, evolving by Langevin dynamics in a channel geometry. This bias controls the degree of particle clustering. On biasing to large clustering, we observe a dynamical phase transition where the particles break symmetry and accumulate at one of the walls. We analyze the mechanical properties of this symmetry-broken state using the Irving-Kirkwood stress tensor. The biased ensemble is characterized by body forces that originate in random thermal noises, but they have finite averages in the presence of the bias. We discuss the connection of these forces to Doob's transform and optimal control theory.