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Model-free detection of physical order from scattering and imaging data using escort-weighted Shannon entropy and divergence matrices

Jared Coles1,2, Arthur R. C. McCray1,3, Yue Li1, Bryan T. Fichera1, Yan Wu4, Yiqing Hao4, Daniel Phelan1, Yue Cao1, Raymond Osborn1 et al.

Charudatta Phatak1,5, Stephan Rosenkranz1, and Yu Li1,*

  • *Contact author: yu.li@anl.gov
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Phys. Rev. Research 8, 033235 – Published 27 August, 2026

DOI: https://doi.org/10.1103/5txt-skp5

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 a physical model or order parameter. We further show that pairwise divergence matrices, in particular, Kullback-Leibler divergence, Jeffrey divergence, Jensen-Shannon divergence, and difference 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 nontrivial phase transition in magnetic skyrmion lattices observed through Lorentz-transition electron microscopy. These results establish a framework for fast, automated, model-free detection of physical order in experimental data with broad applications in materials science and condensed matter physics.

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Phys. Rev. Research 8, 033235– Published 27 August, 2026
  • Received 28 January 2026
  • Accepted 27 July 2026
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