Pressure and Phase Equilibria in Interacting Active Brownian Spheres

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 $P$.

6p (main text) + 4p (SI)

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• Applicability of Effective Pair Potentials for Active Brownian Particles
• Non-Equilibrium Surface Tension of the Vapour-Liquid Interface of Active Lennard-Jones Particles
• Active Brownian particles at interfaces: An effective equilibrium approach
• Kinetics of motility-induced phase separation and swim pressure
• Interparticle torques suppress motility-induced phase separation for rodlike particles
• Swimming to Stability: Structural and Dynamical Control via Active Doping
• Nonequilibrium phase behaviour from minimization of free power dissipation
• Green-Kubo approach to the average swim speed in active Brownian systems
• Liquid-gas transitions in steady heat conduction
• How statistical forces depend on thermodynamics and kinetics of driven media
• Lack of an equation of state for the nonequilibrium chemical potential of gases of active particles in contact
• Three-body correlations and conditional forces in suspensions of active hard disks
• Zeroth law of thermodynamics for nonequilibrium steady states in contact
• Colloidal Brazil nut effect in microswimmer mixtures induced by motility contrast
• Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise