Mean-Squared Energy Difference for Exploring Potential Energy Landscapes of Supercooled Liquids

By extending the concept of diffusion to the potential energy landscapes (PELs), we introduce the mean-squared energy difference (MSED) as a novel quantity to investigate the intrinsic properties of supercooled liquids. MSED can provide a clear description of the ``energy relaxation'' process on a PEL. Through MSED analysis, we have obtained a characteristic time similar to that derived from structure analysis, namely \tau_\alpha^\ast. Further, we establish a connection between MSED and the feature of PELs, providing a concise and quantitative description of PELs. The relaxation behavior of energy has been found to follow a stretched exponential form. As the temperature decreases, the roughness of the accessible PEL changes significantly around a characteristic temperature T_x, which is 20% higher than the glass transition temperature T_\rm g and is comparable to the critical temperature of the mode-coupling theory. More importantly, one of the PEL parameters is closely related to the Adam-Gibbs configurational entropy. The present research, which directly links the PEL to the relaxation process, provides avenues for further research of glasses.