Quantum engines and the range of the second law of thermodynamics in the   noncommutative phase-space
  Two testable schemes for quantum heat engines are investigated under the quantization framework of noncommutative (NC) quantum mechanics (QM). By identifying the phenomenological connection between the phase-space NC driving parameters and an effective external magnetic field, the NC effects on the efficiency coefficient, \mathcal{N} , of quantum engines can be quantified for two different cycles: an isomagnetic one and an isoenergetic one. In addition, paying a special attention to the quantum Carnot cycle, one notices that the inclusion of NC effects does not affect the maximal (Carnot) efficiency, \mathcal{N}^C, ratifying the robustness of the second law of thermodynamics. 
Jonas F. G. Santos and Alex E. Bernardini
quant-ph hep-th