Construction and Optimization of the Quantum Analog of Carnot Cycles

The quantum analog of Carnot cycles in few-particle systems consists of two quantum adiabatic steps and two isothermal steps. This construction is formally justified by use of a minimum work principle. It is then shown, without relying on any microscopic interpretations of work or heat, that the heat-to-work efficiency of the quantum Carnot cycle thus constructed may be further optimized, provided that two conditions regarding the expectation value of some generalized force operators evaluated at equilibrium states are satisfied. In general the optimized efficiency is system-specific, lower than the Carnot efficiency, and dependent upon both temperatures of the cold and hot reservoirs. Simple computational examples are used to illustrate our theory. The results should be an important guide towards the design of favorable working conditions of a realistic quantum heat engine.