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In a recent study by some of us, we have proposed a new measure of thestructure of a liquid, the softness of the mean-field caging potential, andshown that it can describe the temperature dependence of the dynamics. In thiswork, we put this parameter through a stringent test and study the causalrelationship between this softness parameter at the local level and the localdynamics. We first extend the earlier study to describe the local softness. Wefind a distribution of the softness value where the distribution has reasonablystrong temperature dependence. This shows that the parameter can identify thelocal structural heterogeneity. We then study the lifetime of the softnessparameter and show that its lifetime is connected to the well-known cagestructure in the supercooled liquids. Finally, our theory predicts that thelocal softness and the local dynamics is causal below the onset temperaturewhere there is a decoupling between the short and long time dynamics, thusallowing a static description of the cage. We find that at lower temperatures,the structural heterogeneity increases, and also, the structure becomes abetter predictor of the dynamics, thus giving rise to dynamic heterogeneity. Wealso find that the softness of a hard, immobile region evolves with time andbecomes soft and eventually mobile due to the rearrangements in theneighbourhood, confirming the well-known facilitation effect.

Identifying structural signature of dynamical heterogeneity via the local softness parameter