Journal of Statistical Physics, Vol. 37, Nos. 5/6, 1984. p. 673-695.
We consider a (deterministic, conservative) one-dimensional system of colored hard points, changing color each time they hit one another with a relative velocity above a threshold. In the limit of rare reactions, the N-particle color distribution follows a Markovian birth-and-death process. Using the reaction rate as an intrinsic time scale, we also obtain the reaction-diffusion equation for a test particle in this hydrodynamic limit. Explicit results are given for a discrete and a Maxwellian velocity distribution.