  The minimal work principle asserts that work done on a thermally isolated
equilibrium system, is minimal for the slowest (adiabatic) realization of a
given process. This principle, one of the formulations of the second law, is
operationally well-defined for any finite (few particle) Hamiltonian system.
Within classical Hamiltonian mechanics, we show that the principle is valid for
a system of which the observable of work is an ergodic function. For
non-ergodic systems the principle may or may not hold, depending on additional
conditions. Examples displaying the limits of the principle are presented and
their direct experimental realizations are discussed.
