  The relaxation properties of viscous liquids close to their glass transition
(GT) have been widely characterised by the statistical tool of time correlation
functions. However, the strong influence of ubiquitous non-linearities calls
for new, alternative tools of analysis. In this respect, information
theory-based observables and, more specifically, mutual information (MI) are
gaining increasing interest. Here, we report on novel, deeper insight provided
by MI-based analysis of molecular dynamics simulations of molecular and
macromolecular glass-formers on two distinct aspects of transport and
relaxation close to GT, namely dynamical heterogeneity (DH) and secondary
Johari--Goldstein (JG) relaxation processes. In a model molecular liquid with
significant DH, MI reveals two populations of particles organised in clusters
having either filamentous or compact globular structures that exhibit different
mobility and relaxation properties. In a model polymer melt, MI provides
clearer evidence of JG secondary relaxation and sharper insight into its DH. It
is found that both DH and MI between the orientation and the displacement of
the bonds reach (local) maxima at the time scales of the primary and JG
secondary relaxation. This suggests that, in (macro)molecular systems, the
mechanistic explanation of both DH and relaxation must involve
rotation/translation coupling.
