On the universality of nonclassical nonlinear phenomena and their classification

Recent discoveries of nonclassical nonlinear effects in materials have suggested the existence of a nonlinear mesoscopic elasticity (NME) universality class. In the present contribution, we go beyond NME and look for the underlying mathematical foundations that may justify conjectured universality. Using a completely general "response box" formalism, we classify the response according to its spectral contents and obtain the analyticity conditions. We prove that, under the assumption of no conditioning, from the result of a single experiment at a certain amplitude A the response of the system to any excitation of the same frequency and amplitude A<A can be derived