  We consider a mixture of passive (i.e., Brownian) and active (e.g., bacterial
or colloidal swimmers) particles, and analyze the stability conditions of
either uniformly mixed or phase segregated steady states consisting of phases
enriched with different types of particles. We show that in sufficiently dilute
mixtures the system behaves as if it were exposed to two separate heat baths of
uneven temperatures. It can be described within a second virial approximation
neglecting three body and higher order collisions. In this approximation, we
define non-equilibrium "chemical potentials" whose gradients govern diffusion
fluxes and a non-equilibrium "osmotic pressure", which governs the mechanical
stability of the interface.
