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In polydisperse systems, describing the structure and any structural orderparameter (SOP) is not trivial as it varies with the number of species we useto describe the system, M . Depending on the degree of polydispersity, there isan optimum value of M = M0 where we show that the mutual information of thesystem increases. However, surprisingly the correlation between a recentlyproposed SOP and the dynamics is highest for M = 1. This effect increases withpolydispersity. We find that the SOP at M = 1 is coupled with the particlesize, {\sigma}, and this coupling increases with polydispersity and decreaseswith an increase in M . Careful analysis shows that at lower polydispersity theSOP is a good predictor of the dynamics. However, at higher polydispersity, thedynamics is strongly dependent on {\sigma}. Since the coupling between the SOPand {\sigma} is higher for M = 1 thus, it appears to be a better predictor ofthe dynamics. We also study the Vibrality an order parameter independent ofstructural information. Compared to SOP, at high polydispersity we findVibrality to be a marginally better predictor of the dynamics. However, thishigh predictive power of Vibrality, which is not there at lower polydispersity,appears to be due to its stronger coupling with {\sigma}. Thus our studysuggests that for systems with high polydispersity, the correlation of anyorder parameter and {\sigma} will affect the correlation between the orderparameter and dynamics and need not project a generic predictive power of theorder parameter.

Dynamic heterogeneity in polydisperse systems: A comparative study of the role of local structural order parameter and particle size