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

TL;DR

This paper introduces a new causation measure based on a fluctuation-response theorem for Kullback-Leibler divergences, linking information theory and physical perturbation propagation.

Contribution

It defines an information-theoretic causation measure with invariance properties, connecting Fisher information, transfer entropy, and physical perturbations.

Findings

The measure is invariant under certain transformations.

In linear systems, it reduces to transfer entropy.

Provides a physical interpretation of causation via perturbation propagation.

Abstract

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.