Effective equilibrium states in mixtures of active particles driven by colored noise

TL;DR

This paper develops an approximate theoretical framework to analyze the steady-state behavior of mixtures of active particles driven by colored noise, enabling insights into phenomena like demixing and depletion.

Contribution

It extends Fox's theory to multi-component active particle systems with colored noise, deriving an approximate Fokker-Planck equation for their configurational distribution.

Findings

The theory accurately predicts distributions for harmonic interactions.

It provides a qualitative description of many-body phenomena like demixing.

The approach is validated against simulations for soft-repulsive interactions.

Abstract

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power laws potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension, and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.