Fluctuation-response theorem for Kullback-Leibler divergences to quantify causation

02/13/2021

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by   Andrea Auconi, et al.

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We define a new measure of causation from a fluctuation-response theorem for Kullback-Leibler divergences, based on the information-theoretic cost of perturbations. This information response has both the invariance properties required for an information-theoretic measure and the physical interpretation of a propagation of perturbations. In linear systems, the information response reduces to the transfer entropy, providing a connection between Fisher and mutual information.