  Starting from second order around thermal equilibrium, the response of a
statistical mechanical system to an external stimulus is not only governed by
dissipation and depends explicitly on dynamical details of the system. The so
called frenetic contribution in second order around equilibrium is illustrated
in different physical examples, such as for non-thermodynamic aspects in the
coupling between system and reservoir, for the dependence on disorder in
dielectric response and for the nonlinear correction to the
Sutherland--Einstein relation. More generally, the way in which a system's
dynamical activity changes by the pertubation is visible (only) from nonlinear
response.
