  Detecting and quantifying causality is a focal topic in the fields of
science, engineering, and interdisciplinary studies. However, causal studies on
non-intervention systems attract much attention but remain extremely
challenging. To address this challenge, we propose a framework named
Interventional Dynamical Causality (IntDC) for such non-intervention systems,
along with its computational criterion, Interventional Embedding Entropy (IEE),
to quantify causality. The IEE criterion theoretically and numerically enables
the deciphering of IntDC solely from observational (non-interventional)
time-series data, without requiring any knowledge of dynamical models or real
interventions in the considered system. Demonstrations of performance showed
the accuracy and robustness of IEE on benchmark simulated systems as well as
real-world systems, including the neural connectomes of C. elegans, COVID-19
transmission networks in Japan, and regulatory networks surrounding key
circadian genes.
