  The fluctuation-dissipation-theorem connects equilibrium to mildly (linearly)
perturbed situations in a thermodynamic manner: It involves the observable of
interest and the entropy production caused by the perturbation. We derive a
relation which connects responses of arbitrary order in perturbation strength
to correlations of entropy production of lower order, thereby extending the
fluctuation-dissipation-theorem to cases far from equilibrium in a
thermodynamic way. The relation is validated and studied for a 4-state-model.
