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Glass formation is encountered in diverse materials. Experiments haverevealed that dynamic relaxation spectra of supercooled liquids genericallybecome asymmetric near the glass transition temperature, $T_g$, where anextended power law emerges at high frequencies. The microscopic origin of this"wing" remains unknown, and was so far inaccessible to simulations. Here, wedevelop a novel computational approach and study the equilibrium dynamics ofmodel supercooled liquids near $T_g$. We demonstrate the emergence of a powerlaw wing in numerical spectra, which originates from relaxation at rare,localised regions over broadly-distributed timescales. We rationalise theasymmetric shape of relaxation spectra by constructing an empirical modelassociating heterogeneous activated dynamics with dynamic facilitation, whichare the two minimal physical ingredients revealed by our simulations. Our workoffers a glimpse of the molecular motion responsible for glass formation atrelevant experimental conditions.

Microscopic origin of excess wings in relaxation spectra of supercooled liquids