{
  "abstract": "We study genuine multi-entropy in Abelian $U(1)_k$ Chern-Simons theory. For key-ring link states, where only the linking numbers between one distinguished component $K$ and the remaining $\\mathtt{q}-1$ components are nonzero, we derive an exact closed-form expression for the $\\mathtt{q}$-partite Rényi multi-entropy for general $\\mathtt{q}$, level $k$, and Rényi index $n$. For $\\mathtt{q}=4$, this shows that the genuine multi-entropy $\\mathrm{GM}^{(4)}_n$ collapses exactly onto the tripartite information $I_{3,n}$ for all $n$, while for $\\mathtt{q}=5$ it is likewise completely determined, for all $n$, by a linear combination of tripartite and bipartite Rényi multi-entropies. We then go beyond the key-ring class and study general four-component link states with arbitrary pairwise linking numbers. A numerical scan over Chern--Simons levels $2\\leq k\\leq24$ shows that the all-$n$ collapse found analytically for key-ring states does not survive for generic link states. Remarkably, the collapse remains exact at $n=2$ for every level examined. At $n=3$, violations occur, within the scanned range, only when $3\\mid k$, with a further dependence on the $3$-adic valuation of $k$. At $n=4$ and $n=5$, violations occur for every level examined, with rates that vary strongly with $k$. These results show that the breakdown is not controlled simply by the zero-divisor structure of composite $\\mathbb Z_k$, but instead exhibits a nontrivial joint dependence on the Rényi index and the arithmetic structure of the Chern--Simons level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29627",
  "author_total": 4,
  "authors": [
    {
      "name": "Yen-Cheng Chang"
    },
    {
      "name": "Kaberi Goswami"
    },
    {
      "name": "Norihiro Iizuka"
    },
    {
      "name": "Akihiro Miyata"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bwrck54aa97s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29627",
  "fulltext_url": null,
  "id": "9bwrck54aa97s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29627",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7204873881",
  "pdf_url": "https://arxiv.org/pdf/2608.29627",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bwrck54aa97s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.29627",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29627"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Genuine Multi-Entropy in Abelian Chern--Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States",
  "title_text": "Genuine Multi-Entropy in Abelian Chern--Simons Theory: Exact Key-Ring Collapse and Its Breakdown for Generic Link States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/9bwrck54aa97s",
  "venue": "arXiv",
  "versions": []
}