  Amorphous solids relax via slow molecular rearrangement induced by thermal
fluctuations or applied stress. Although microscopic structural signatures
predicting these structural relaxations have long been sought, a physically
motivated structural measure relevant to diverse systems remains elusive. Here,
we introduce a structural order parameter derived from the mean-field caging
potential experienced by the particles due to their neighbors, which reliably
predicts the occurrence of structural relaxations. The parameter, derived from
density functional theory, is a measure of susceptibility to particle
rearrangements that can effectively identify weak or defect-like regions in
disordered systems. Using experiments on dense colloidal suspensions, we
demonstrate a causal relationship between this order parameter and the
structural relaxations of the amorphous solid. In quiescent suspensions,
increasing the density leads to stronger correlations between the structure and
dynamics. Under applied shear, the mean structural order parameter increases
with increasing strain, signaling shear-induced softening, which is accompanied
by the proliferation of plastic events. In both cases, the order parameter
reliably identifies weak regions where the plastic rearrangements due to
thermal fluctuation or applied shear preferentially occur. Our study paves the
way to a structural understanding of the relaxation of a wide range of
amorphous solids, from suspensions to metallic glasses.
