Identifying structural signature of dynamical heterogeneity via the local softness parameter

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