 The non-additive entropy SQ has been introduced in 1988 focusing on a generalization of Boltzmann-Gibb's, BG, statistical mechanics. The aim was to cover a, possibly wide, class of systems among those very many which violate hypothesis such as ergodicity, under which BG theory is expected to be valid. We review and comment some relevant aspects of this entropy, namely additivity versus extensivity. This article was authored by Konstantino Tsalis.