Abstract
We study a driven particle system whose velocity distribution f(v,t) satisfies a Boltzmann equation with a nonlinear collision term, and linear terms representing collisions with thermalized particles of another species having a specified Maxwellian distribution, and a driving force. We prove that when the nonlinear terms dominate, f(v,t) is kept close to a Maxwellian distribution M(v;u(t),e(t)) with parameters u(t) and e(t) satisfying a system of nonlinear equations-the ''hydrodynamic'' equations. This result holds even when their stationary solution is nonunique, corresponding to a dynamical phase transition for f in such systems. We apply our results to a model of a partially ionized spatially homogeneous plasma in an external field E.