Minimal-work principle and its limits for classical systems

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 nonergodic 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.