  A relation between vibrational entropy and particles mean square displacement
is derived in super-cooled liquids, assuming that the main effect of
temperature changes is to rescale the vibrational spectrum. Deviations from
this relation, in particular due to the presence of a Boson Peak whose shape
and frequency changes with temperature, are estimated. Using observations of
the short-time dynamics in liquids of various fragility, it is argued that (i)
if the crystal entropy is significantly smaller than the liquid entropy at
$T_g$, the extrapolation of the vibrational entropy leads to the correlation
$T_K\approx T_0$, where $T_K$ is the Kauzmann temperature and $T_0$ is the
temperature extracted from the Vogel-Fulcher fit of the viscosity. (ii) The
jump in specific heat associated with vibrational entropy is very small for
strong liquids, and increases with fragility. The analysis suggests that these
correlations stem from the stiffening of the Boson Peak under cooling,
underlying the importance of this phenomenon on the dynamical arrest.
