Interacting particles in an activity landscape

TL;DR

This paper investigates how active Brownian particles behave in environments with spatially varying activity levels, revealing unique nonequilibrium phenomena and conditions for phase separation.

Contribution

It introduces a theoretical and simulation framework for ABPs in activity landscapes, showing the breakdown of mechanical equilibrium and the conditions for phase separation.

Findings

An equation of state exists but does not imply mechanical equilibrium.

Pressure differences are due to fluxes of polar order and activity gradients.

No critical point for phase separation in activity patches unless density is very high.

Abstract

We study interacting active Brownian particles (ABPs) with a space-dependent swim velocity via simulation and theory. We find that, although an equation of state exists, a mechanical equilibrium does not apply to ABPs in activity landscapes. The pressure difference originates in the flux of polar order and the gradient of swim velocity across the interface between regions of different activity. In contrast to motility-induced phase separation of ABPs with a homogeneous swim velocity, a critical point does not exist for an active-passive patch system, which continuously splits into a dense and a dilute phase with increasing activity. However, if the global density is so high that not all particles can be packed onto the inactive patch, then MIPS-like behavior is restored and the pressure is balanced again.