Different constructions and optimization of the irreversible quantum Carnot cycle

The irreversible Carnot cycle is designed, constructed and optimized for quantum systems with non-scalable energy levels. In the cycle, the thermalization strokes are interpreted as either energy conserving steps or quantum isochoric processes. It is found that the latter construction is necessary to optimize the irreversible cycle efficiency. A strict connection between the two interpretations is given in terms of the irreversible entropy production and the efficiency lag. Two spins 1/2 interacting within the Heisenberg XXX model under a tunable magnetic field are proposed as the working system of the irreversible cycle. It is found that the irreversible cycle efficiency is always below the classical Carnot efficiency and depends on the parameters of the working medium and the heat baths. The role of the reservoir temperatures and the interaction between the spins on the efficiency is revealed. Quantum coupling is found to have a destructive role on the cycle performance which decreases the efficiency and makes the Carnot cycle cease to operate as a heat engine after a critical value. System parameter regimes are revealed where the optimized cycle efficiency is close to or notably higher than the one that conserves the energy in the thermalization stages.