Do short-time fluctuations predict the long-time dynamic heterogeneity in a supercooled liquid?

Recent investigations have demonstrated that the short-time fluctuations in a supercooled liquid can be used as predictors of the long-time dynamic propensity (that is, the regions of the sample with enhanced tendency to be mobile within time scales on the order of the alpha-relaxation time). This could mean that the long-time dynamics (the actual mobility of the particles at such long times) would be implicit in the short-time dynamics or else, that the long-time dynamic propensity [as defined in A. Widmer-Cooper and P. Harrowell, Phys. Rev. Lett. 96, 185701 (2006)], while providing a measure of the degree of jamming of the local structure, would only be sensitive to the short time behavior. The first scenario is in clear disagreement with our recent finding that the influence of the local structure on dynamics (as determined by the propensity for motion) is only local in time, fading out at times close to the metabasin lifetime, much before the alpha-relaxation time. Thus, in this work we show that the short-time fluctuations in supercooled liquids do in fact represent precursors to the dynamics at intermediate times commensurate with the metabasin lifetime (being thus able to predict the regions of the sample that will present high propensity for motion at such stage) but that the dynamical behavior at later times of the alpha relaxation is unpredictable, in agreement with a metabasin random walk scenario.