Multidimensional measures of response and fluctuations in stochastic dynamical systems

A class of experiments is proposed which involve multiple measurements combined with multiple perturbations of a nonlinear classical complex system. A family of multipoint n + m - 1 dimensional measures R((n, m)) that provide complementary information on complex systems is obtained by combining m nonlinear stimuli and n measurements. They represent the combined effect of causal response and noncausal spontaneous fluctuations. The proposed signals can be measured either in the frequency domain or in the time domain. Generalized fluctuation-dissipation relations which hold in the nonlinear regime restrict the number of independent techniques. Two-dimensional correlation plots derived from such measurements can reveal various types of couplings among collective modes.