  Nonlinear response theory, in contrast to linear cases, involves (dynamical)
details, and this makes application to many body systems challenging. From the
microscopic starting point we obtain an exact response theory for a small
number of coarse grained degrees of freedom. With it, an extrapolation scheme
uses near-equilibrium measurements to predict far from equilibrium properties
(here, second order responses). Because it does not involve system details,
this approach can be applied to many body systems. It is illustrated in a four
state model and in the near critical Ising model.
