New solutions to scale-invariant phase-space occupancy for the generalized entropy Sq

We extend a class of solutions reported by Tsallis, Gell-Mann, and Sato [C. Tsallis, M. Gell-Mann, Y. Sato, Asymptotically-scale-invariant occupancy of phase space makes the entropy Sq extensive, Proc. Natl. Acad. Sci. (2005), in press] for specially correlated binary systems exhibiting scale-invariant phase space occupancy. Limitations of the validity of all solutions are analyzed in detail showing that as the number of binary systems grows, the validity of solutions is limited to the trivial case p=1.