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Measuring EEGs as a complex system using entropies is a very fruitful approach. It reveals hidden properties of the observed system without knowing it's internal structure and topology.
It can discriminate walking state, sleeping state, epilepsy and even deepness of narcosis.
It is a very useful approach used even in cardiology and ECGs.
1) Entropies for detection of epilepsy in EEG - ScienceDirect