Multidimensional Stationary Probability Distribution for Interacting Active Particles

TL;DR

This paper develops a multidimensional theoretical framework to describe the stationary distribution of active particles under colored noise, validated by simulations, revealing insights into particle accumulation, contact probabilities, and pressure in non-equilibrium systems.

Contribution

It introduces a multidimensional Unified Colored Noise Approximation to analytically describe active particle distributions in non-equilibrium settings.

Findings

Quantitative agreement between theory and simulations for particle accumulation.

Probability of particle contact decreases when one particle is pinned.

Derived an equation of state for active particles based on the theory.

Abstract

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density quantitatively describes the accumulation of active particles around repulsive obstacles. In particular, for two particles with repulsive interactions, the probability of close contact decreases when one of the two particle is pinned. Moreover, in the case of isotropic confining potentials, the radial density profile shows a non trivial scaling with radius. Finally we show that the theory well approximates the "pressure" generated by the active particles allowing to derive an equation of state for a system of non-interacting colored noise-driven particles.