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The Liouville equation differs from the von Neumann equation 'only' by acharacteristic superoperator. We demonstrate this for Hamiltonian dynamics, ingeneral, and for the Jaynes-Cummings model, in particular. -- Employingsuperspace (instead of Hilbert space), we describe time evolution of densitymatrices in terms of path integrals which are formally identical for quantumand classical mechanics. They only differ by the interaction contributing tothe action. This allows to import tools developed for Feynman path integrals,in order to deal with superoperators instead of quantum mechanical commutatorsin real time evolution. Perturbation theory is derived. Besides applications inclassical statistical physics, the "classical path integral" and the parallelstudy of classical and quantum evolution indicate new aspects of (dynamicallyassisted) entanglement (generation). Our findings suggest to distinguish'intra'- from 'inter-space' entanglement.

A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide