  Starting from a microscopic model of self-propelled hard spheres we use tools
of non-equilibrium statistical mechanics and the kinetic theory of hard spheres
to derive a Smoluchowski equation for interacting Active Brownian particles. We
illustrate the utility of the statistical mechanics framework developed with
two applications. First, we derive the steady state pressure of the hard sphere
active fluid in terms of the microscopic parameters and second, we identify the
critical density for the onset of motility-induced phase separation in this
system. We show that both these quantities agree well with overdamped
simulations of active Brownian particles with excluded volume interactions
given by steeply repulsive potentials. The results presented here can be used
to incorporate excluded volume effects in diverse models of self-propelled
particles.
