{
  "abstract": "We develop a cohomological framework for entanglement entropy that unifies information theory, operator algebras, and noncommutative geometry. Entropy is a 1-cocycle in information cohomology; we generalize this to the quantum setting via Hochschild and cyclic cohomology. For an inclusion of von Neumann algebras N contained in M with a faithful normal state w admitting a cyclic and separating vector, and a conditional expectation E: M -> N (whose existence is equivalent to modular invariance of N by Takesaki's theorem), we construct the entanglement complex as the image of the transgression map tau_w on the relative cyclic complex, where A is a dense *-subalgebra of M and B = A intersect N. Our main result identifies entanglement cohomology with the kernel of the restriction map HC*(A) -> HC*(B), up to the connecting homomorphism d of the long exact sequence of the pair (A,B); when d = 0, the identification is exact. The relative modular cocycle u_t = (Dw : D(w|_N) o E)_t generates explicit entanglement classes when E is not w-invariant, with the Araki relative entropy as its infinitesimal generator. The framework accommodates Type III von Neumann algebras, where no local density matrix exists, and leads to a holographic proposal: a subspace of H^1_ent is conjecturally dual to linearized modular Hamiltonian perturbations of the bulk entanglement wedge. We verify the construction in finite-dimensional, type II_1, and type III_1 examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17195",
  "author_total": 1,
  "authors": [
    {
      "name": "R. C. Rashkov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7p4k1w5cb7src.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17195",
  "fulltext_url": null,
  "id": "7p4k1w5cb7src",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17195",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213421003",
  "pdf_url": "https://arxiv.org/pdf/2609.17195",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7p4k1w5cb7src.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2609.17195",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17195"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Cohomological Aspects of Entanglement Entropy: From Information Theory to Noncommutative Geometry",
  "title_text": "Cohomological Aspects of Entanglement Entropy: From Information Theory to Noncommutative Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/7p4k1w5cb7src",
  "venue": "arXiv",
  "versions": []
}