Impact of fluctuations on particle systems described by Dean-Kawasaki-type equations

TL;DR

This paper investigates how fluctuations influence particle systems modeled by Dean-Kawasaki equations, revealing that noise can enhance propagation, accelerate pattern formation, and reduce hysteresis, thus playing a constructive role.

Contribution

It demonstrates that conserved multiplicative noise in Dean-Kawasaki models can significantly alter macroscopic behaviors, highlighting the importance of stochastic effects in particle dynamics.

Findings

Noise increases front propagation speed in density-dependent systems.

Fluctuations accelerate pattern formation in nonlocal interaction models.

Hysteresis is reduced by fluctuations in systems with repulsive forces.

Abstract

We study the role of fluctuations in particle systems modeled by Dean-Kawasaki-type equations, which describe the evolution of particle densities in systems with Brownian motion. By comparing microscopic simulations, stochastic partial differential equations, and their deterministic counterparts, we analyze four models of increasing complexity. Our results identify macroscopic quantities that can be altered by the conserved multiplicative noise that typically appears in the Dean-Kawasaki-type description. We find that this noise enhances front propagation speed in systems with density-dependent diffusivity, accelerates the onset of pattern formation in particle systems with nonlocal interactions, and reduces hysteresis in systems interacting via repulsive forces. In some cases, it accelerates transitions or induces structures absent in deterministic models. These findings illustrate that (conservative) fluctuations can have constructive and nontrivial effects, emphasizing the importance of stochastic modeling in understanding collective particle dynamics.