  The scaling of the slow structural relaxation with the fast caged dynamics is
evidenced in the molten salt Ca_{0.4}K_{0.6}(NO_{3}$)_{1.4} (CKN) over about
thirteen decades of the structural relaxation time. Glycerol caling was
analyzed in detail. In glycerol, the short-time mean-square displacement <u^2>,
a measure of the caged dynamics, is contributed by free-volume. It is seen
that, in order to evidence the scaling, the observation time of the fast
dynamics must be shorter than the time scales of the relaxation processes.
Systems with both negligible (like CKN, glycerol and network glassformers) and
high (like van der Waals liquids and polymers) pressure-energy correlations
exhibit the scaling between the slow relaxation and the fast caged dynamics.
According to the available experiments, an isomorph-invariant expression of the
master curve of the scaled data is not distinguishable from a simpler
not-invariant expression. Instead, the latter grees better with the simulations
on a wide class of model polymers.
