  We report the complete statistical treatment of a system of particles
interacting via Newtonian forces in continuous boundary-driven flow, far from
equilibrium. By numerically time-stepping the force-balance equations of a
model fluid we measure occupancies and transition rates in simulation. The
high-shear-rate simulation data verify the invariant quantities predicted by
our statistical theory, thus demonstrating that a class of non-equilibrium
steady states of matter, namely sheared complex fluids, is amenable to
statistical treatment from first principles.
