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.Comment: version accepted for publication in J. Stat. Phy
