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Cyclic thermodynamic processes and entropy production

Walid K. Abou Salem·Juerg Froehlich
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Abstract

We study the time evolution of a periodically driven quantum-mechanical system coupled to several reserviors of free fermions at different temperatures. This is a paradigm of a cyclic thermodynamic process. We introduce the notion of a Floquet Liouvillean as the generator of the dynamics on an extended Hilbert space. We show that the time-periodic state to which the true state of the coupled system converges 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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Walid K. Abou Salem, Juerg Froehlich. 2006-04-23. Cyclic thermodynamic processes and entropy production. https://arxiv.org/abs/math-ph/0601043

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