Pressure and Phase Equilibria in Interacting Active Brownian Spheres

TL;DR

This paper derives an exact expression for the mechanical pressure in active Brownian particles, revealing its dependence on bulk correlations and implications for phase separation, independent of wall interactions.

Contribution

It provides a first-principles derivation of pressure in active Brownian systems, showing it as a state function and clarifying its role in phase coexistence.

Findings

Pressure is a state function, independent of wall interactions.

Interactions contribute two distinct terms to pressure.

Coexisting phases have equal pressure, but densities do not follow Maxwell construction.

Abstract

We derive from first principles the mechanical pressure $P$, defined as the force per unit area on a bounding wall, in a system of spherical, overdamped, active Brownian particles at density $\rho$. Our exact result relates $P$, in closed form, to bulk correlators and shows that (i) $P(\rho)$ is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to $P$, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; (iii) $P(\rho)$ is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles, and show that the densities at coexistence do not satisfy a Maxwell construction on $P$.