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In this manuscript we present a comparative study about the determination ofthe relaxation (\textit{i.e.}, independence) time scales obtained from thecorrelation function, the mutual information, and a criterion based on theevaluation of a nonextensive generalisation of mutual entropy. Our results showthat, for systems with a small degree of complexity, standard mutualinformation and the criterion based on its nonextensive generalisation providethe same scale, whereas for systems with a higher complex dynamics the standardmutual information presents a time scale consistently smaller.

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