Ideal bulk pressure of active Brownian particles

TL;DR

This paper investigates the pressure in an ideal active Brownian particle system, distinguishing between mechanical and local bulk pressures, and examines how boundary effects influence these pressures in different geometries.

Contribution

It provides analytical insights into the difference between mechanical and local bulk pressures and how boundary effects impact pressure measurements in active matter systems.

Findings

Boundary effects control correlations affecting mechanical pressure.

A local bulk pressure exists and differs from the mechanical pressure.

Virial formula accurately predicts mechanical pressure in simple geometries.

Abstract

The extent to which active matter might be described by effective equilibrium concepts like temperature and pressure is currently being discussed intensely. Here we study the simplest model, an ideal gas of non-interacting active Brownian particles. While the mechanical pressure exerted onto confining walls has been linked to correlations between particles' positions and their orientations, we show that these correlations are entirely controlled by boundary effects. We also consider a definition of local pressure, which describes interparticle forces in terms of momentum exchange between different regions of the system. We present three pieces of analytical evidence which indicate that such a local pressure exists, and we show that its bulk value differs from the mechanical pressure exerted on the walls of the system. We attribute this difference to the fact that the local pressure in the bulk does not depend on boundary effects, contrary to the mechanical pressure. We carefully examine these boundary effects using a channel geometry, and we show a virial formula for the pressure correctly predicts the mechanical pressure even in finite channels. However, this result no longer holds in more complex geometries, as exemplified for a channel that includes circular obstacles.