Fluctuations, correlations and the nonextensivity

Examples of joint probability distributions are studied in terms of Tsallis' nonextensive statistics both for correlated and uncorrelated variables, in particular it is explicitely shown how correlations in the system can make Tsallis entropy additive and that the effective nonextensivity parameter $q_N$ decreases towards unity when the number of variables $N$ increases. We demonstrate that Tsallis distribution of energies of particles in a system leads in natural way to the Negative Binomial multiplicity distribution in this system.