The Complete Solution to the Glass Transition: A Unified Energy–Topology Landscape (ETL) Framework

Abstract

The glass transition — the dramatic dynamical arrest of supercooled liquids into amorphous solids — remains one of the deepest unsolved problems in condensed-matter physics. Competing paradigms (thermodynamic Random First-Order Transition [RFOT], kinetically constrained/facilitation models, frustration-based approaches, and energy landscape viewpoints) each capture facets of the phenomenon but fail to produce a single, predictive, experimentally falsifiable theory. Here I propose the Energy–Topology Landscape (ETL) Unification, a theoretical and computational framework that synthesizes thermodynamics, topology of configuration space, and dynamical facilitation into a single continuum theory. In ETL the glass transition is not a single mechanism but an emergent consequence of (1) a proliferation of high-dimensional topological bottlenecks in the potential-energy landscape as cooling proceeds, (2) a finite but vanishingly small measure of accessible configuration-space pathways that enforce hierarchical facilitation, and (3) a thermodynamic drift toward deep meta-basins whose internal ruggedness controls low-temperature vibrational anomalies. ETL yields closed-form scaling relations for relaxation times, a microscopic origin for the boson peak and non-linear elastic response, and precise experimental signatures (specific heat, non-linear susceptibility, ultrastable glass fingerprints). I provide a mathematical formalism, numerical algorithmic recipes, and a program of decisive experiments. I argue that, once the proposed predictions are verified (or falsified) by the community, the ETL framework will constitute a comprehensive resolution to the glass problem.