# Anisotropic Structural Predictor in Glassy Materials

## TL;DR

This paper introduces a tensorial structural predictor based on local heat capacity and its directional response, improving the prediction of plastic rearrangements in glassy materials by accounting for anisotropic softness.

## Contribution

It derives a first-principles tensorial measure of softness in glasses, capturing anisotropic responses and enhancing the prediction of plastic events.

## Key findings

- The linear response of local heat capacity follows a fat-tailed distribution.
- The tensorial predictor outperforms scalar measures in predicting plastic rearrangements.
- The predictor accounts for orientation-dependent coupling to external deformation.

## Abstract

There is a growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to quantify their degree of softness. These softness measures, however, are typically scalars, not taking into account the tensorial/anisotropic nature of soft spots, which implies orientation-dependent coupling to external deformation. Here we derive from first principles the linear response coupling between the local heat capacity of glasses, previously shown to provide a measure of glassy softness, and external deformation in different directions. We first show that this linear response quantity follows an anomalous, fat-tailed distribution related to the universal $\omega^4$ density of states of quasilocalized, nonphononic excitations in glasses. We then construct a structural predictor as the product of the local heat capacity and its linear response to external deformation, and show that it offers enhanced predictability of plastic rearrangements under deformation in different directions, compared to the purely scalar predictor.