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An approximate nonlinear-response theory is derived by maximizing the information theoretic entropy in the space of fluctuations J(t) of the degree of freedom of interest, subject to constant-energy dissipation in the external field. The resulting formalism expresses all cumulant averages of J(t) in an external field in terms of equilibrium cumulants.
Jeppe C. Dyre (Tue,) studied this question.