  An attempt toward the operational formulation of quantum thermodynamics is
made by employing the recently proposed operations forming positive
operator-valued measures for generating thermodynamic processes. The quantity
of heat as well as the von Neumann entropy monotonically increases under the
operations. The fixed point analysis shows that repeated applications of these
operations to a given system transform from its pure ground state at zero
temperature to the completely random state in the high temperature limit with
intermediate states being generically out of equilibrium. It is shown that the
Clausius inequality can be violated along the processes, in general. A
bipartite spin-1/2 system is analyzed as an explicit example.
