  We re-interprete the microcanonical conditions in the quantum domain as
constraints for the interaction of the "gas-subsystem" under consideration and
its environment ("container"). The time-average of a purity-measure is found to
equal the average over the respective path in Hilbert-space. We then show that
for typical (degenerate or non-degenerate) thermodynamical systems almost all
states within the allowed region of Hilbert-space have a local von
Neumann-entropy S close to the maximum and a purity P close to its minimum,
respectively. Typically thermodynamical systems should therefore obey the
second law.
