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In the study of thermodynamics for nanoscale quantum systems, a family of quantities known as generalized free energies have been derived as necessary and sufficient conditions that govern state transitions.
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N. H. Y. Ng, L. Mančinska, C. Cirstoiu, J. Eisert, and S. Wehner, “Limits to catalysis in quantum thermodynamics,” New Journal of Physics
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2017
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