Multidimensional Measures of Response and Fluctuations in Stochastic Dynamical Systems

A new 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⁽ that provide complimentary information on complex systems is obtained by combining m non linear 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.