A quantum-mechanical heat engine operating in finite time. A model consisting of spin-1/2 systems as the working fluid

The finite‐time operation of a quantum‐mechanical heat engine with a working fluid consisting of many noninteracting spin‐1/2 systems is considered. The engine is driven by an external, time‐dependent and nonrotating magnetic field. The cycle of operation consists of two adiabats and two isotherms. The analysis is based on the time derivatives of the first and second laws of thermodynamics. Explicit relations linking quantum observables to thermodynamic quantities are developed. The irreversible operation of this engine is studied in three cases: (1) The sudden limit, where the performance is found to be the same as that of the spin analog of the Otto cycle. This case provides the lower bound of efficiency. (2) The step‐cycle operation scheme. Here, the optimization of power is carried out in the high‐temperature limit (the ‘‘classical’’ limit). The results obtained are similar to those of Andresen et al. [Phys. Rev. A 15, 2086 (1977)]. (3) The Curzon–Ahlborn operation scheme. The semigroup approach is us...