Statistical complexity of potential energy landscape as a dynamic signature of the glass transition

Dynamic heterogeneity is an intrinsic characteristic of amorphous materials that is closely related to the mysterious glass transition. However, there is seldom an intuitive physical parameter characterizing the degree of dynamic heterogeneity and linking it quantitatively to the dynamic arrest phenomenon at the glass transition. Here, we propose a general theoretical protocol to explain the glass transition via a statistical parameter quantifying the dynamic heterogeneity of glass-forming systems. The parameter can be calculated using the concept of the Shannon information entropy associated with the variation in the activation barriers to local structural excitations on the underlying potential energy landscape, which can be explored extensively using the recently developed activation-relaxation technique in inherent structures spanning a wide range of configurational space. The concept is demonstrated successfully in a model of a prototypical glass-forming system ${\mathrm{Cu}}_{50}{\mathrm{Zr}}_{50}$. The Shannon entropy and statistical variation in the activation barriers are found to change dramatically at the glass-to-liquid transition and, therefore, can be treated as a novel signature of the glass transition, beyond the conventional thermodynamic indicators, such as the volume, potential energy, enthalpy, and heat capacity. The temperature-dependent Shannon entropy coincides with the evolution of the experimentally available stretching exponent during the glass-to-liquid transition and provides an intuitive explanation for the obscure decrease in dynamic heterogeneity from a metastable glass to an equilibrium liquid. Finally, possible relationships among structures, thermodynamics, and dynamics are discussed in terms of quantitative correlations among the structural Shannon entropy, excess total entropy, and dynamic Shannon entropy, respectively.