Starting from a microscopic model of self-propelled hard spheres we use toolsof non-equilibrium statistical mechanics and the kinetic theory of hard spheresto derive a Smoluchowski equation for interacting Active Brownian particles. Weillustrate the utility of the statistical mechanics framework developed withtwo applications. First, we derive the steady state pressure of the hard sphereactive fluid in terms of the microscopic parameters and second, we identify thecritical density for the onset of motility-induced phase separation in thissystem. We show that both these quantities agree well with overdampedsimulations of active Brownian particles with excluded volume interactionsgiven by steeply repulsive potentials. The results presented here can be usedto incorporate excluded volume effects in diverse models of self-propelledparticles.
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