  We treat a quantum mechanical system with certain general properties which
are expected to be common in macroscopic quantum systems. Starting from a PURE
initial state (which may not describe an equilibrium) in which energy is mildly
concentrated at a single value, we consider a time evolution determined by a
time-dependent Hamiltonian as a model of an adiabatic operation in
thermodynamics. We take a family of operations with the same procedure and
various ``waiting times.'' Then the Minimum Work Principle is rigorously proved
for almost all choices of the waiting time.
