A New Kind Of Quantum Heat Engine

We reformulate the first law of thermodynamics in terms of quantum-mechanical operators on the parameter manifold. We introduce a class of quantum heat engine which consists of two-level systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle.Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Some of the results above can be generalized to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's daemon.Finally we introduce a quantum heat engine, in which the working medium is a quantum system with a discrete level and a continuum. Net work clone by this engine is calculated and discussed. The results show that this quantum heat engine behaves like the two-level quantum heat engine in both the high-temperature and the low-temperature limits, but it operates differently in temperatures between them. The efficiency of this quantum heat engine is also presented and discussed.