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By subjecting a dynamical system to a series of short pulses and varyingseveral time delays we can obtain multidimensional characteristic measures ofthe system. Multidimensional Kullback-Leibler response function (KLRF), whichare based on the Kullback-Leibler distance between the initial and finalstates, are defined. We compare the KLRF, which are nonlinear in theprobability density, with ordinary response functions (ORF) obtained from theexpectation value of a dynamical variable, which are linear. We show that theKLRF encode different level of information regarding the system's dynamics. Foroverdamped stochastic dynamics two dimensional KLRF shows a qualitativelydifferent variation with the time delays between pulses, depending on whetherthe system is initially in a steady state, or in thermal equilibrium.

Multidimensional measures of impulsively driven stochastic systems based on the Kullback-Leibler distance