Multidimensional Stationary Probability Distribution for Interacting Active Particles

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.

5 pages, 2 figures

References in corpus (10)

• Statistical Mechanics of Interacting Run-and-Tumble Bacteria
• Diffusive transport without detailed balance in motile bacteria: Does microbiology need statistical physics?
• Pressure and Phase Equilibria in Interacting Active Brownian Spheres
• Sedimentation, trapping, and rectification of dilute bacteria
• Generalized energy equipartition in harmonic oscillators driven by active baths
• Differential Dynamic Microscopy: a High-Throughput Method for Characterizing the Motility of Microorganism
• Tunable long range forces mediated by self-propelled colloidal hard spheres
• Clustering and heterogeneous dynamics in a kinetic Monte-Carlo model of self-propelled hard disks
• Directed transport of active particles over asymmetric energy barriers
• Filling an emulsion drop with motile bacteria