Quasi-additivity of Tsallis entropies and correlated subsystems

We use Beck's quasi-additivity of Tsallis entropies for n   independent subsystems to show that like the case of n=2$n=2$, the entropic index q$q$ approaches 1 by increasing system size. Then, we will generalize that concept to correlated subsystems to find that in the case of correlated subsystems, when system size increases, q$q$ also approaches a value corresponding to the additive case.