The very purpose of a control system is to pump information out of the relationship between the variable under control and the influences acting on it. This results in zero correlation between variables that are directly causally connected, and large (above 0.99) correlations between variables that are causally connected only via those zero-correlation links. I have a paper on the subject.
This remains true even if correlation (generally meant in the linear product-moment sense) is replaced by the more general concept of statistical dependence (non-zero mutual information).
The graphs describing such systems contain cycles, so the apparatus of causal analysis based on DAGs does not apply.
The very purpose of a control system is to pump information out of the relationship between the variable under control and the influences acting on it. This results in zero correlation between variables that are directly causally connected, and large (above 0.99) correlations between variables that are causally connected only via those zero-correlation links. I have a paper on the subject.
This remains true even if correlation (generally meant in the linear product-moment sense) is replaced by the more general concept of statistical dependence (non-zero mutual information).
The graphs describing such systems contain cycles, so the apparatus of causal analysis based on DAGs does not apply.