  In this manuscript we present a comparative study about the determination of
the relaxation (\textit{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.
