  The concept of internal friction, a fully quantum mechanical phenomena, is
investigated in a simple, experimentally accessible quantum system in which a
spin-1/2 is driven by a transverse magnetic field in a quantum adiabatic
process. The irreversible production of the waste energy due to the quantum
friction is quantitatively analyzed in a forward-backward unitary transform of
the system Hamiltonian by using the quantum relative entropy between the actual
density matrix obtained in a parametric transformation and the one in a
reversible adiabatic process. Analyzing the role of total transformation time
and the different pulse control schemes on the internal friction reveal the
non-monotone character of the internal friction as a function of the total
protocol time and the possibility for almost frictionless solutions in
finite-time transformations.
