The present study introduces a renormalization-based approach to investigate the relaxation dynamics within supercooled liquids. By applying a numerical scale transformation to potential energies along the temporal axis, we have established a novel framework that elucidates the underlying kinetics of supercooled liquids. Our findings indicate that the skewness of the potential energy distribution attains its maximum at a characteristic time scale $\left({\mathrm{\Delta }}_{\mathrm{CTS}}\right)$, which exhibits a scaling law with temperature [${\mathrm{\Delta }}_{\mathrm{CTS}}\propto {\left(T-T^{*}\right)}^{-\gamma }$]. This scaling relationship is characterized by an exponent $\gamma$ that experiences a discontinuous transition at a critical cooling rate, signifying a kinetic-like phase transition. We further find that the product of $\gamma$ and the logarithm of the cooling rate is approximately constant. This constant, however, varies depending on whether the cooling rate is above or below the critical value, effectively classifying supercooled liquids into two regimes: a glass-forming regime (GFR) and a crystal-forming regime (CFR). Furthermore, we identify that $T^{*}$ corresponds to the glass transition temperature for GFR $\left(T_g\right)$ and the crystallization temperature for CFR $\left(T_c\right)$, respectively. We have successfully developed a theoretical model, which not only derives the scaling law but also provides profound insights into the physical implications of ${\mathrm{\Delta }}_{\mathrm{CTS}}$, $\gamma$, and $T^{*}$. This research delineates the differences between GFR and CFR and offers a fresh perspective for exploring the nature of glasses. The findings contribute to the broader understanding of the dynamics of supercooled liquids and the mechanisms of glass formation.

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• Glass transition
• Glasses
• Supercooled liquid
• Molecular dynamics