A simple quantum heat engine

A simple urn model is presented that may describe heat engines employing as working agents spin2 particles (e.g., electrons) or twolevel atoms. In this model the cold reservoir is an urn located at altitude ǫc that contains N balls of total weight nc. Likewise, the hot reservoir at altitude ǫh contains N balls of total weight nh. A cycle consists of exchanging two randomly selected balls between the reservoirs. Elementary considerations show that the heat-engine efficiency (ratio of the average work performed divided by the average hot-reservoir energy consumption) is η = 1 − ǫc/ǫh. The case where the two reservoirs have negative temperatures is symmetrical to the case where the two reservoirs have positive temperatures in the sense that heat engines become heat pumps and conversely. When the cold reservoir has positive temperature while the hot reservoir has negative temperature the maximum efficiency is unity. When many cold and hot sub-reservoirs (of the same temperature signs) are employed the Carnot efficiency may be reached. For some parameter values the work performed does not fluctuate from cycle to cycle. Mas Liron, F30440 Saint Martial, France Centre d’Électronique et de Micro-optoélectronique de Montpellier, Unité Mixte de Recherche n5507 au CNRS, Université Montpellier II, F34095 Montpellier, France Département de Mathématiques et Informatique Appliquées, Université Paul Valéry, F34199 Montpellier, France. Also with LIRMM, 161 rue Ada, F34392 Montpellier, France