Geometric Encoding of Thermal History in Glasses: Strain Topology as a Learnable Structural Signature

The glass transition poses a fundamental question in condensed matter physics: how does thermal history become encoded in the atomic structure of disordered solids? Here we demonstrate that the memory of cooling rate is geometrically encoded in the strain topology the spatial distribution of local mechanical distortions rather than in simple density or coordination metrics. Using graph neural networks (GNNs) as structural probes and a systematic ablation methodology on a Lennard-Jones model system, we achieve 95% classification accuracy between fast-cooled and slow-cooled glasses with full geometric information, and maintain 90-94% accuracy even when feature magnitudes are instance-normalized to remove trivial separability. Pure topological features (connectivity alone) fail at near-random accuracy (52%), while local Hessian eigenvalues and bond-length distributions together carry the discriminative signal. Beyond classification, we show that GNNs can partially recover ordered initial geometries from thermally scrambled glasses with approximately 7-8% reconstruction error. Mapping reconstruction fidelity as a function of scrambling duration reveals a sharp transition: geometric memory collapses abruptly within 500 scrambling steps and plateaus thereafter, consistent with rapid correlation-length fragmentation in this model system. Visualization of strain-weighted contact networks confirms the physical picture fast-cooled glasses exhibit fragmented, short-range stress patterns, while slow-cooled glasses develop extended, percolating force chains. These results establish that thermal history manifests as a learnable geometric pattern written in bond-strain distributions, with the specific signature depending on material composition and interaction potential.