Counter-intuitive properties of a simple quantum heat engine.

We show that a quantum heat engine operating between two thermal baths may exhibit unusual responses to changes in the baths' temperatures. For example, its thermodynamic efficiency may increase as their temperature difference decreases. Conversely, the engine may cease to operate if the hotter bath becomes too hot, or the colder bath too cold, even in the limit of absolute zero temperature. Moreover, in some circumstances it may run in either sense of the same thermodynamic cycle, with the physical heat reservoirs exchanging the roles of `hot' or `cold' bath. In these cases there is a `temperature gap': a finite range of temperatures for one of the baths within which no engine is possible, and on either side of which the engine runs in opposite senses. We demonstrate these and other counter-intuitive phenomena using a simple model of a quantum Otto cycle whose `working substance' is a pair of spins coupled by the isotropic Heisenberg interaction. Quantum correlations play no role in these effects, which are due solely to the structure of the energy spectrum. We explain many of them, and also previously reported efficiency gains exhibited by this model, using a simple physical picture in terms of energy flows via each system level.