Nonlinear-response theory for time-independent fields: Consequences of the fractal nonequilibrium distribution function

Classical nonlinear-response theory is applied to an ensemble of experiments performed under the same external field. If the field is time independent, the formalism simplifies, and we can derive the ``Kawasaki expression'' for the distribution function, as well as the transient correlation-function expression for the observable response. Recent computer simulations have shed new light on our understanding of the steady-state nonequilibrium distribution function: the fractal nature of the distribution causes us to reevaluate the usual mathematical tools used to describe nonequilibrium processes.