  Non-extensive systems do not allow to go to the thermodynamic limit.
  Therefore we have to reformulate statistical mechanics without invoking the
thermodynamical limit. I.e. we have to go back to Pre-Gibbsian times. We show
that Boltzmann's mechanical definition of entropy S as function of the
conserved ``extensive'' variables energy E, particle number N etc. allows to
describe even the most sophisticated cases of phase transitions unambiguously
for ``small'' systems like nuclei, atomic clusters, and selfgravitating
astrophysical systems: The rich topology of the curvature of S(E,N) shows the
whole ``Zoo'' of transitions: transitions of 1.order including the surface
tension at phase-separation, continuous transitions, critical and
multi-critical points. The transitions are the ``catastrophes'' of the Laplace
transform from the ``extensive'' to the ``intensive'' variables. Moreover, this
classification of phase transitions is much more natural than the Yang-Lee
criterion.
