Potential energy landscape description with Gamma distribution for supercooled liquids and glasses

Hongqin Liu

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arXiv · 2512.20792

Potential energy landscape description with Gamma distribution for supercooled liquids and glasses

Hongqin Liu

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Abstract

The potential energy landscape, PEL, theory stands as one of the most successful frameworks for understanding supercooled liquids and glassy systems. A central element of this theory is the configurational entropy, Sc, which is traditionally represented by a symmetric Gaussian distribution. However, the asymmetric nature of the potential energy of inherent structures, Eis, poses a challenge to such a representation across wide regions of configurational space. In addition, the Gaussian distribution fails to represent fragile to strong transition, FST, observed in various fluids. In this work, we demonstrate that an asymmetric distribution, specifically the Gamma distribution, provides effective description of both Sc and Eis over broad ranges of density and temperature, T. The FST is interpreted through shifts of the Eis distribution and the curvature change of the Eis vs 1/T relation. In terms of energy changes, the FST is comparable to a liquid-liquid phase transition. Moreover, the revised PEL framework yields an equation of state that incorporates a singular term diverging at a glassy or jammed state, an important feature for accurately describing the pressure behavior of these systems.

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Hongqin Liu. 2025-12-23. Potential energy landscape description with Gamma distribution for supercooled liquids and glasses. https://arxiv.org/abs/2512.20792

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