  We describe our recent proposal of a path integral formulation of classical
Hamiltonian dynamics. Which leads us here to a new attempt at hybrid dynamics,
which concerns the direct coupling of classical and quantum mechanical degrees
of freedom. This is of practical as well as of foundational interest and no
fully satisfactory solution of this problem has been established to date.
Related aspects will be observed in a general linear ensemble theory, which
comprises classical and quantum dynamics in the form of Liouville and von
Neumann equations, respectively, as special cases. Considering the simplest
object characterized by a two-dimensional state-space, we illustrate how
quantum mechanics is special in several respects among possible linear
generalizations.
