  We discuss the response of aging systems with short-range interactions to a
class of random perturbations. Although these systems are out of equilibrium,
the limit value of the free energy at long times is equal to the equilibrium
free energy. By exploiting this fact, we define a new order parameter function,
and we relate it to the ratio between response and fluctuation, which is in
principle measurable in an aging experiment. For a class of systems possessing
stochastic stability, we show that this new order parameter function is
intimately related to the static order parameter function, describing the
distribution of overlaps between clustering states. The same method is applied
to investigate the geometrical organization of pure states. We show that the
ultrametric organization in the dynamics implies static ultrametricity, and we
relate these properties to static separability, i.e., the property that the
measure of the overlap between pure states is essentially unique. Our results,
especially relevant for spin glasses, pave the way to an experimental
determination of the order parameter function.
