Active hard-spheres in infinitely many dimensions

TL;DR

This paper provides an exact analysis of active hard-spheres in infinite dimensions, revealing their stationary properties, phase behavior, and crowding effects without relying on equilibrium assumptions.

Contribution

It introduces an exact solution for active hard-spheres in infinite dimensions, enabling the study of nonequilibrium stationary states and phase separation phenomena.

Findings

Exact structure factor and pressure equation of state

Accounted motility-induced phase separation

Determined crowding density where propulsion vanishes

Abstract

Few equilibrium --even less so nonequilibrium-- statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical hard-spheres in infinitely many space dimensions are a notable exception. We show that even without resorting to a Boltzmann distribution, dimensionality is a powerful organizing device to explore the stationary properties of active hard-spheres evolving far from equilibrium. In infinite dimensions, we compute exactly the stationary state properties that govern and characterize the collective behavior of active hard-spheres: the structure factor and the equation of state for the pressure. In turn, this allows us to account for motility-induced phase-separation. Finally, we determine the crowding density at which the effective propulsion of a particle vanishes.