  A single driven spin is investigated as the working substance of a six-stroke
irreversible quantum Carnot cycle. The role of inner friction associated with
the finite-time adiabatic transformations on the cycle efficiency and the
harvested work are investigated in detail. The inner friction is found to
significantly reduce the work output and the cycle efficiency which can make
the engine incapable to produce positive work for the too fast adiabatic
transformations. The ideal Carnot efficiency is found to be reached only for
the quasi-static transformations. A deviation of the cycle efficiency from the
classical Carnot efficiency has been given by an efficiency lag which is
directly related to the total entropy production due to the inner friction. The
released heat in the relaxation processes of the cycle are associated with the
entropy production and the inner friction. The extension of the results for a
scale invariant quantum working substance and the possible experimental
implementation of the irreversible quantum Carnot cycle in a liquid state
nuclear magnetic resonance setup are also discussed.
