  The minimal work principle states that work done on a thermally isolated
equilibrium system is minimal for adiabatically slow (reversible) realization
of a given process. This principle, one of the formulations of the second law,
is studied here for finite (possibly large) quantum systems interacting with
macroscopic sources of work. It is shown to be valid as long as the adiabatic
energy levels do not cross. If level crossing does occur, counter examples are
discussed, showing that the minimal work principle can be violated and that
optimal processes are neither adiabatically slow nor reversible. The results
are corroborated by an exactly solvable model.
