  Boltzmann's principle S(E,N,V)=k*ln W(E,N,V) relates the entropy to the
geometric area e^{S(E,N,V)} of the manifold of constant energy in the N-body
phase space. From the principle all thermodynamics and especially all phenomena
of phase transitions and critical phenomena can be deduced. The topology of the
curvature matrix C(E,N) (Hessian) of S(E,N) determines regions of pure phases,
regions of phase separation, and (multi-)critical points and lines. Thus,
C(E,N) describes all kind of phase-transitions with all their flavor. No
assumptions of extensivity, concavity of S(E), or additivity have to be
invoked. Thus Boltzmann's principle and not Tsallis statistics describes the
equilibrium properties as well the approach to equilibrium of extensive and
non-extensive Hamiltonian systems. No thermodynamic limit must be invoked.
