An approximate relation between the vibrational entropy and the mean square displacement of the particles is derived. 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 Tg, the extrapolation of the vibrational entropy leads to the correlation TK T0, where TK is the Kauzmann temperature and T0 is the temperature extracted from the Vogel-Fulcher fit of the viscosity, and (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. © 2010 The American Physical Society.