Model-free Analysis of Scattering and Imaging Data with Escort-Weighted Shannon Entropy and Divergence Matrices

TL;DR

This paper introduces a model-free data analysis method using escort-weighted Shannon entropy and divergence matrices to detect phase transitions in scattering and imaging data, applicable across various physical systems.

Contribution

It presents a novel framework that connects physical and informational entropy, enabling sensitive detection of phase transitions without physical models or order parameters.

Findings

Successfully detects phase transitions in neutron and X-ray scattering data.

Identifies a non-trivial phase transition in magnetic skyrmion lattices.

Shows divergence matrices outperform scalar entropy in change detection.

Abstract

We demonstrate a model-free data analysis framework that leverages escort-weighted Shannon Entropy and several divergence matrices to detect phase transitions in scattering and imaging datasets. By establishing a connection between physical entropy and informational entropy, this approach provides a sensitive method for identifying phase transitions without an explicit physical model or order parameter. We further show that pairwise divergence matrices, including Kullback-Leibler divergence, Jeffrey Divergence, Jensen-Shannon Divergence and antisymmetric Kullback-Leibler divergence, provide more comprehensive measures of statistical changes than scalar entropy alone. Our approach successfully detects the onset of both long- and short-range order in neutron and X-ray scattering data, as well as a non-trivial phase transition in magnetic skyrmion lattices observed through Lorentz-transition electron microscopy. These results establish a framework for automated, model-free analysis of experimental data with broad applications in materials science and condensed matter physics.