We report the application of a far-from-equilibrium statistical-mechanical theory to a nontrivial system with Newtonian interactions in continuous boundary-driven flow. By numerically time stepping the force-balance equations of a one-dimensional model fluid we measure occupancies and transition rates in simulation. The high-shear-rate simulation data reproduce the predicted invariant quantities, thus supporting the theory that a class of nonequilibrium steady states of matter, namely, sheared complex fluids, is amenable to statistical treatment from first principles.