Understanding causation via correlations and linear response theory
Statistical Mechanics
2021-01-04 v1
Abstract
In spite of the (correct) common-wisdom statement correlation does not imply causation, a proper employ of time correlations and of fluctuation-response theory allows to understand the causal relations between the variables of a multi-dimensional linear Markov process. It is shown that the fluctuation-response formalism can be used both to find the direct causal links between the variables of a system and to introduce a degree of causation, cumulative in time, whose physical interpretation is straightforward. Although for generic non-linear dynamics there is no simple exact relationship between correlations and response functions, the described protocol can still give a useful proxy also in presence of weak nonlinear terms.
Cite
@article{arxiv.2010.01522,
title = {Understanding causation via correlations and linear response theory},
author = {Marco Baldovin and Fabio Cecconi and Angelo Vulpiani},
journal= {arXiv preprint arXiv:2010.01522},
year = {2021}
}