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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Replicated liquid theory in 1 + ∞ dimensions.

Yukihiro Tomita¹, Hajime Yoshino^1,2

¹Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan.

The Journal of Chemical Physics

|December 8, 2025

Summary

We present a new theory for structural glasses with spatial variations. This approach yields an exact free-energy functional and predicts unique glass order parameter profiles near transitions.

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Area of Science:

Physics
Condensed Matter Physics
Statistical Mechanics

Background:

Structural glasses exhibit complex behavior, including spatial variations in physical quantities.
Understanding glass transitions and associated length scales is crucial in condensed matter physics.

Purpose of the Study:

Develop an exact replicated liquid theory for structural glasses with spatial variations along one axis.
Investigate diverging lengths in dynamic and static glass transitions for hard spheres.
Analyze the spatial profile of the glass order parameter within confining cavities.

Main Methods:

Formulate a replicated liquid theory valid in the limit of infinite transverse dimensions.
Derive an exact free-energy functional incorporating a space-dependent glass order parameter, Δab(z).
Apply the theory to hard sphere systems with and without confining cavities.

Main Results:

The theory provides an exact free-energy functional for spatially varying structural glasses.
Calculated exponents for diverging lengths match previous mean-field model results.
Predicted a non-trivial spatial profile for the glass order parameter within cavities, showing scaling behavior near the glass transition.

Conclusions:

The developed replicated liquid theory offers an exact framework for studying spatially inhomogeneous structural glasses.
The findings provide insights into glass transition dynamics and spatial heterogeneity.
The theory's predictions align with existing models and offer new predictions for confined systems.