The second law of thermodynamics and quantum heat engines: Is the law strictly enforced?

A quantum heat engine is a construct having a working medium which is cyclically processed through a pair of control variables of state involving a Bose–Einstein condensation (BEC) in which a heat input is converted into a work output. Of interest is a first species of quantum heat engine in which the working medium is macroscopic in the sense the size scale is sufficiently large that the BEC is not volumetrically coherent. In this first species of quantum heat engine, near Carnot efficiencies may be possible. Of particular interest is a second species of quantum heat engine in which the working medium is mesoscopic in the sense that the size scale is sufficiently small that the BEC is volumetrically coherent. In this second species of quantum heat engine, the resulting in-process non-equilibrium condition affects the finally arrived at control variables of state such that Carnot efficiencies and beyond may be possible. A Type I superconductor is used to model the first and second species of quantum heat engine.