{
  "abstract": "Phase transitions can generate intricate spatial organization invisible to spatially averaged probes, yet quantitative measures of this organization remain limited. Here we develop \"entropy imaging,\" an information-theoretic technique that harnesses lossless compression to quantify spatial complexity, predictability, and order in quantum materials. Using this approach, emergent spatial textures can be imaged and converted into an experimentally-accessible observable: the computable information density (CID), a compression-based measure of information complexity that approaches the Shannon entropy rate in the large-system limit. Applied to millikelvin microwave impedance microscopy of graphene, the method reveals a pronounced maximum in the CID near quantum Hall transitions, a quantitative measure of the information-rich spatial organization of the critical landscape. A disordered Hofstadter model reproduces this behavior and shows that the CID can identify the quantum critical point from a sequence of images, without ensemble averaging over disorder realizations. The same framework tracks fractional quantum Hall transitions and resolves isolated fractional puddles that coexist with a disordered background. By contrast, the trivial band-edge crossover in a MoSe2/WS2 moiré heterobilayer exhibits qualitatively different behavior, suggesting that the pronounced CID enhancement observed at the quantum Hall critical point is not simply a generic feature of a conductive-insulating crossover. We further show that the geometric information encoded in CID is not reducible to a correlation length, and it can even distinguish spatial textures with identical multifractal statistics. Together, these results establish lossless compression as a framework for quantifying emergent spatial organization in quantum materials, with portability across imaging modalities and physical systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35790",
  "author_total": 16,
  "authors": [
    {
      "name": "Chen Wu"
    },
    {
      "name": "Leonard W. Cao"
    },
    {
      "name": "Lingyuan Lyu"
    },
    {
      "name": "Liam Cohen"
    },
    {
      "name": "Jiahui Nie"
    },
    {
      "name": "Can Uzundal"
    },
    {
      "name": "Yujia Hu"
    },
    {
      "name": "Quanjin Wang"
    },
    {
      "name": "Ziying Yan"
    },
    {
      "name": "Sneh Pancholi"
    },
    {
      "name": "Kenji Watanabe"
    },
    {
      "name": "Takashi Taniguchi"
    },
    {
      "name": "Feng Wang"
    },
    {
      "name": "Andrea F. Young"
    },
    {
      "name": "Tarun Grover"
    },
    {
      "name": "Monica T. Allen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8n79wxceytjdh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35790",
  "fulltext_url": null,
  "id": "8n79wxceytjdh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35790",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.mtrl-sci"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3107|Quantum and electron transport phenomena"
    ]
  ],
  "openalex": "W7223822656",
  "pdf_url": "https://arxiv.org/pdf/2610.35790",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8n79wxceytjdh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35790",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35790"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Information-theoretic entropy imaging of quantum matter",
  "title_text": "Information-theoretic entropy imaging of quantum matter",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/8n79wxceytjdh",
  "venue": "arXiv",
  "versions": []
}