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, the entropic index 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 also approaches a value corresponding to the additive case.