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A microscopically reversible kinetic theory of flocking

We formulate a kinetic theory of two species of hard spheres undergoing reactive collisions that convert chemical energy into kinetic energy. The model describes an active species interacting with a passive background, labeled as birds and air respectively, with the reactive collisions representing of self-propulsion. Microscopic reversibility of the reactive dynamics is imposed, and a chemostat is introduced to drive the system out of equilibrium. When the chemostat is sufficiently strong and one restricts to grazing interspecies collisions, we find that the bird momentum damping coefficient can change sign, giving rise to a flocking transition.