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Near the glass point molecules wander much faster than this rule predicts, and a quantitative explanation is missing.","posed_since":"","precise":"Near $T_g$ in molecular liquids such as o-terphenyl, $D\\eta/T$ exceeds its high-temperature value by roughly two to three orders of magnitude (approximate), and $D\\sim \\tau_{\\alpha}^{-\\xi}$ with a fractional exponent reported near 0.75 to 0.85. Predict the magnitude, temperature dependence and exponent $\\xi$ from a theory of dynamic heterogeneity, and explain why rotational diffusion follows viscosity more closely than translational diffusion.","problem_ref":null,"references":"","settled_by":"A theory that predicts $D(T)$, $\\eta(T)$ and the decoupling exponent for a model liquid and agrees with simulations and with measurements on molecular glass formers.","status_note":"Attribution of the decoupling to dynamic heterogeneity is widely accepted qualitatively, but a quantitative prediction of the exponent is lacking (2026).","title":"Why diffusion decouples from viscosity near the glass 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