# The second laws of quantum thermodynamics

@article{Brando2015TheSL, title={The second laws of quantum thermodynamics}, author={Fernando G. S. L. Brand{\~a}o and Michal Horodecki and Nelly Huei Ying Ng and Jonathan Oppenheim and Stephanie Wehner}, journal={Proceedings of the National Academy of Sciences}, year={2015}, volume={112}, pages={3275 - 3279} }

Significance In ordinary thermodynamics, transitions are governed by a single quantity–the free energy. Its monotonicity is a formulation of the second law. Here, we find that the second law for microscopic or highly correlated systems takes on a very different form than it does at the macroscopic scale, imposing not just one constraint on state transformations, but many. We find a family of quantum free energies which generalize the standard free energy, and can never increase. The ordinary…

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