  An extensively studied mechanism to create particle-antiparticle asymmetries
is the out-of-equilibrium and CP violating decay of a heavy particle. Here we
instead examine how asymmetries can arise purely from 2 <-> 2 annihilations
rather than from the usual 1 <-> 2 decays and inverse decays. We review the
general conditions on the reaction rates that arise from S-matrix unitarity and
CPT invariance, and show how these are implemented in the context of a simple
toy model. We formulate the Boltzmann equations for this model, and present an
example solution.
