Composite systems with extensive Sq (power-law) entropies

The problem of characterizing the kind of correlations leading to an extensive behaviour of the Sq (power-law) entropic measure has recently been considered by Tsallis, Gell-Mann and Sato (TGS) [Complexity and Non-Extensivity: New Trends in Statistical Mechanics, Yukawa Institute, Kyoto, 14-18 March 2005]. We propose a family of models for the probability occupancy of phase space exhibiting an extensive behaviour of Sq and allowing for an explicit analysis of the N→∞ (thermodynamic) limit.