  We investigate the correlations of initially separable probability
distributions in a globally pure bipartite system with two degrees of freedom
for classical and quantum systems. A classical version of the quantum linear
mutual information is introduced and the two quantities are compared for a
system of oscillators coupled with both linear and non-linear interactions. The
classical correlations help to understand how much of the quantum loss of
purity are due to intrinsic quantum effects and how much is related to the
probabilistic character of the initial states, a characteristic shared by both
the classical and quantum pictures. Our examples show that, for initially
localized Gaussian states, the classical statistical mutual linear entropy
follows its quantum counterpart for short times. For non-Gaussian states the
behavior of the classical and quantum measures of information are still
qualitatively similar, although the fingerprints of the non-classical nature of
the initial state can be observed in their different amplitudes of oscillation.
