Steady states, invariant measures, and response theory

Using the method of computer simulation we test the predictions of nonlinear response theory for classical systems subject to dissipative external fields. We provide convincing numerical evidence that Kawasaki methods agree with both the transient time correlation function predictions and with a direct measurement of the nonlinear response. Furthermore, this numerical agreement is observed over a time scale which is sufficiently long for the response to have relaxed to within {~}1% of its nonequilibrium steady-state value. This is in spite of the fact that in the steady state the N-particle distribution function ultimately becomes fractal. We discuss the normalization of the Kawasaki distribution and derive a ``Lagrangian form'' of the Kawasaki response function, and show that it is consistent with predictions that are obtained using a natural invariant measure for nonequilibrium steady states.