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Asymptotically scale-invariant occupancy of phase space makes the entropy Sq extensive
Phase space can be constructed for equal and distinguishable subsystems
that could be (probabilistically) either {\it weakly} (or {\it "locally"})
correlated (e.g., independent, i.e., uncorrelated), or {\it strongly} (or {\it
globally}) correlated. If they are locally correlated, we expect the
Boltzmann-Gibbs entropy to be {\it
extensive}, i.e., for . In particular, if
they are independent, is {\it strictly additive}, i.e., . However, if the subsystems are globally correlated, we
expect, for a vast class of systems, the entropy (with ) for some special value of to be the
one which extensive (i.e., for ).Comment: 15 pages, including 9 figures and 8 Tables. The new version is
considerably enlarged with regard to the previous ones. New examples and new
references have been include
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