{
  "abstract": "Towards a question of Voiculescu, two notions of $1$-bounded entropy, $h$ and $h^\\text{top}$, are defined for $C^*$-algebras. The quantity $h$ involves the tracial completion with respect to all traces while the quantity $h^\\text{top}$ depends on operator norm microstates. It is demonstrated that $h^\\text{top}(\\mathscr{A})$ does not exceed $h(\\mathscr{A})$ for all $C^*$-algebras $\\mathscr{A}$. Moreover, a variational principle enabling the computation of $h$ is introduced. The quantity $h$ is computed in various examples, and the computation is used to justify structural conclusions such as $C^*$-primeness, crossed product indecomposability, and free indecomposability. These notions of entropy are generalized to operator systems, where it is demonstrated that both may be computed on a basis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.15409",
  "author_total": 1,
  "authors": [
    {
      "name": "Connor MacMahon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ch3w2tpedx5s4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.15409",
  "fulltext_url": null,
  "id": "ch3w2tpedx5s4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.15409",
  "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",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7203696130",
  "pdf_url": "https://arxiv.org/pdf/2608.15409",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ch3w2tpedx5s4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.15409",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.15409"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "1-Bounded Entropy for $C^*$-Algebras",
  "title_text": "1-Bounded Entropy for C^*-Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ch3w2tpedx5s4",
  "venue": "arXiv",
  "versions": []
}