  Equilibrium statistics of Hamiltonian systems is correctly described by the
microcanonical ensemble. Classically this is the manifold of all points in the
$N-$body phase space with the given total energy. Due to Boltzmann's principle,
$e^S=tr(\delta(E-H))$, its geometrical size is related to the entropy
$S(E,N,...)$. This definition does not invoke any information theory, no
thermodynamic limit, no extensivity, and no homogeneity assumption, as are
needed in conventional (canonical) thermo-statistics. Therefore, it describes
the equilibrium statistics of extensive as well of non-extensive systems. Due
to this fact it is the {\em fundamental} definition of any classical
equilibrium statistics. It can address nuclei and astrophysical objects as
well. All kind of phase transitions can be distinguished sharply and uniquely
for even small systems. For transitions in nuclear physics the scaling to an
hypothetical uncharged nuclear matter with an $N/Z-$ ratio like realistic
nuclei is not needed.
