  The correspondence principle plays a fundamental role in quantum mechanics,
which naturally leads us to inquire whether it is possible to find or determine
close classical analogs of quantum states in phase space -- a common meeting
point to both classical and quantum density statistical descriptors. Here, this
issue is tackled by investigating the behavior of classical analogs arising
upon the removal of all interference traits displayed by the Wigner
distribution functions associated with a given pure quantum state. Accordingly,
the dynamical evolution of the linear and von Neumann entropies is numerically
computed for a continuous-variable bipartite system, and compared with the
corresponding classical counterparts, in the case of two quartic oscillators
nonlinearly coupled under regular and chaos conditions. Three quantum states
for the full system are considered: a Gaussian state, a cat state, and a
Bell-type state. By comparing the quantum and classical entropy values, and
particularly their trends, it is shown that, instead of entanglement
production, such entropies rather provide us with information on the system
(either quantum or classical) delocalization. This gradual loss of information
translates into an increase in both the quantum and the classical realms,
directly connected to the increase in the correlations between both parties'
degrees of freedom which, in the quantum case, is commonly related to the
production of entanglement.
