{
  "abstract": "We address an open problem raised by Polyanskiy and Wu in their textbook concerning the subadditivity of mutual \\(f\\)-information. We study two notions of generalized mutual information: mutual \\(f\\)-information, defined by \\(\\widetilde{I}_f(X;Y)=D_f(p_{XY}\\|p_Xp_Y)\\), and variational \\((G,f)\\)-information, obtained by minimizing an average of transformed \\(f\\)-divergences. For the first notion, we derive a sufficient condition on \\(g(x)=x^2f''(x)\\) that guarantees subadditivity under conditionally independent observations. This condition yields explicit families beyond the previously known examples generated by \\(x\\log x\\) and \\((x-1)\\log x\\). Our proof relies on the concavity of a generalized variance functional. For the variational notion, we extend existing sufficient conditions beyond the transforms \\(G(x)\\in\\{x,\\log(1+x),-\\log(1-x)\\}\\). Using a comparison inequality for \\(G^{-1}(G(A)+G(B))\\), we obtain differential criteria for concave and convex transforms. Explicit constructions illustrate the resulting classes of subadditive information measures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21231",
  "author_total": 2,
  "authors": [
    {
      "name": "Hamidreza Abin"
    },
    {
      "name": "Amin Gohari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7x966bzs53v29.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21231",
  "fulltext_url": null,
  "id": "7x966bzs53v29",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21231",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "3109|Statistical Mechanics and Entropy"
    ]
  ],
  "openalex": "W7222579195",
  "pdf_url": "https://arxiv.org/pdf/2610.21231",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7x966bzs53v29.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21231",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21231"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Statistical Mechanics and Entropy",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "On the Subadditivity of Mutual f-Information",
  "title_text": "On the Subadditivity of Mutual f-Information",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/7x966bzs53v29",
  "venue": "arXiv",
  "versions": []
}