Emergence of directed motion in a crowded suspension of overdamped particles with different effective temperatures

In this work, we focus on the behavior of a single passive Brownian particle in a suspension of passive particles with short-range repulsive interactions and higher effective temperature. While the forces affecting the single particle are thermal-like fluctuations and repulsion, due to other particles in the suspension, our numerical simulations show that on intermediate timescales directed motion on a single-particle level emerges. This emergent directional motion leads to a breakdown of the Einstein relation and nonmonotonic augmentation of the measured diffusion coefficient. Directional tendency increases with the density of the suspension and leads to growth of the diffusivity with the density of the suspension, a phenomenon recently observed for a system of hard spheres by Ilker, Castellana, and Joanny. Counterintuitively, the directional flow originates from the tendency of different particles to push each other out of their way. Due to such strictly repulsive interactions, nearby particles form into temporally correlated pairs and move cooperatively, thus creating a preferred direction of motion on intermediate timescales. We show that directional motion emerges when the ratio of the effective temperatures of the tracked particle and suspension constituents is below a critical value.