  In this work we generalize and combine Gibbs and von Neumann approaches to
build, for the first time, a rigorous definition of entropy for hybrid
quantum-classical systems. The resulting function coincides with the two cases
above when the suitable limits are considered. Then, we apply the MaxEnt
principle for this hybrid entropy function and obtain the natural candidate for
the Hybrid Canonical Ensemble (HCE). We prove that the suitable classical and
quantum limits of the HCE coincide with the usual classical and quantum
canonical ensembles since the whole scheme admits both limits, thus showing
that the MaxEnt principle is applicable and consistent for hybrid systems.
