Image Source: Proceedings of the National Academy of Sciences |

**ABSTRACT**

*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, 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, N*

^{C}, ratifying the robustness of the second law of thermodynamics.Quantum engines and the range of the second law of thermodynamics in the noncommutative phase-space

Jonas F. G. Santos, Alex E. Bernardini, Physics arXiv

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