Correlated Gaussian systems exhibiting additive power-law entropies

We show, on purely statistical grounds and without appeal to any physical model, that a power-law $q-$entropy $S_q$, with $0<q<1$, can be {\it extensive}. More specifically, if the components $X_i$ of a vector $X \in $\mathbb{R}$^N$aredistributedaccordingtoaGaussianprobabilitydistribution$f$,theassociatedentropy$S_q(X)$ exhibits the extensivity property for special types of correlations among the $X_i$. We also characterize this kind of correlation.