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

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.

References in corpus (13)

• Measuring Information Transfer
• Granger causality and transfer entropy are equivalent for Gaussian variables
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Nonequilibrium Thermodynamics of Feedback Control
• Information flow between stock indices
• Information Flows? A Critique of Transfer Entropies
• Quantifying causal influences
• Field Theories for Learning Probability Distributions
• Decision Making in the Arrow of Time
• Response theory: a trajectory-based approach
• Understanding causation via correlations and linear response theory
• Continuous information flow fluctuations
• Causal influence in linear response models