  We introduce a new measure of the structure of a liquid which is the softness
of the mean-field potential developed by us earlier. We find that this softness
is sensitive to small changes in the structure. We then study its correlation
with the supercooled liquid dynamics. The study involves a wide range of
liquids (fragile, strong, attractive, repulsive, and active) and predicts some
universal behaviours like the softness is linearly proportional to the
temperature and inversely proportional to the activation barrier of the
dynamics with system dependent proportionality constants. We write down a
master equation between the dynamics and the softness parameter and show that
indeed the dynamics when scaled by the temperature and system dependent
parameters show a data collapse when plotted against softness. The dynamics of
fragile liquids show a strong softness dependence whereas that of strong
liquids show a much weaker softness dependence. We also connect the present
study with the earlier studies of softness involving machine learning (ML) thus
providing a theoretical framework for understanding the ML results.
