On a comparative study between dependence scales determined by linear and non-linear measures

In this manuscript we present a comparative study about the determination of the relaxation ($\mathit{\text{i.e.}}$, independence) time scales obtained from the correlation function, the mutual information, and a criterion based on the evaluation of a nonextensive generalisation of mutual entropy. Our results show that, for systems with a small degree of complexity, standard mutual information and the criterion based on its nonextensive generalisation provide the same scale, whereas for systems with a higher complex dynamics the standard mutual information presents a time scale consistently smaller.