05-436 Walid. K. Abou Salem and Juerg Froehlich

Cyclic thermodynamic processes and entropy production (560K, postscript) Dec 22, 05

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Abstract. We study the time evolution of a periodically driven quantum-mechanical system coupled to several reservoirs of free fermions at different temperatures and chemical potentials. This is a paradigm of a cyclic thermodynamic process. We introduce the notion of a Floquet Liouvillean as the generator of the dynamics of the coupled system on an extended Hilbert space. We show that the time-periodic state which the true state of the coupled system converges to after very many periods corresponds to a zero-energy resonance of the Floquet Liouvillean. We then show that the entropy production per cycle is (strictly) positive, a property that implies Carnot's formulation of the second law of thermodynamics.

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