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The pressure of suspensions of self-propelled objects is studiedtheoretically and by simulation of spherical active Brownian particles (ABP).We show that for certain geometries, the mechanical pressure as force/area of aconfined systems can equally be expressed by bulk properties, which implies theexistence of an nonequilibrium equation of state. Exploiting the virialtheorem, we derive expressions for the pressure of ABPs confined by solid wallsor exposed to periodic boundary conditions. In both cases, the pressurecomprises three contributions: the ideal-gas pressure due to white-noise randomforces, an activity-induce pressure (swim pressure), which can be expressed interms of a product of the bare and a mean effective propulsion velocity, andthe contribution by interparticle forces. We find that the pressure ofspherical ABPs in confined systems explicitly depends on the presence of theconfining walls and the particle-wall interactions, which has no correspondencein systems with periodic boundary conditions. Our simulations ofthree-dimensional APBs in systems with periodic boundary conditions reveal apressure-concentration dependence that becomes increasingly nonmonotonic withincreasing activity. Above a critical activity and ABP concentration, a phasetransition occurs, which is reflected in a rapid and steep change of thepressure. We present and discuss the pressure for various activities andanalyse the contributions of the individual pressure components.

Virial pressure in systems of active Brownian particles