  Equilibrium statistics of Hamiltonian systems is correctly described by the
microcanonical ensemble, whereas canonical ones fail in the most interesting,
mostly inhomogeneous, situations like phase separations or away from the
thermodynamic ``limit'' (e.g. self-gravitating systems and small quantum
systems). A new derivation of the Second Law is presented that respects these
fundamental complications. Our ``geometric foundation of Thermo-Statistics''
opens the fundamental (axiomatic) application of Thermo-Statistics to
non-diluted systems or to ``non-simple'' systems which are not similar to
(homogeneous) fluids. Supprisingly, but also understandably, a so far open
problem c.f. Uffink: cond-mat/0005327, page 50 and page 72.
