{
  "abstract": "This study focuses on conditional entropy frameworks based on the Kolmogorov--Nagumo (KN) mean. First, $(η, ψ)$-KN averaging (\\texttt{EPKNAVG}), a KN-mean extension of the $η$-averaging (\\texttt{EAVG}) framework for $(η, F)$-entropies, is introduced and proven to be equivalent to \\texttt{EAVG} under suitable concavification conditions. Second, motivated by generalized $g$-vulnerability, a new framework is proposed for generalized $g$-conditional entropies. This framework captures conditional entropies beyond the scope of \\texttt{EAVG}-type representations. In particular, it is shown that there exists an $α$ and a joint probability distribution $p_{X, Y}$ such that the Augustin--Csisz{\\' a}r conditional entropy $H_α^{\\mathrm{C}}(X|Y)$ cannot be represented by any $(η,F)$-entropy satisfying \\texttt{EAVG}. In contrast, it is represented within the proposed framework. Furthermore, sufficient conditions are derived under which the proposed generalized $g$-conditional entropies satisfy the conditioning reduces entropy property and the data-processing inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.07624",
  "author_total": 2,
  "authors": [
    {
      "name": "Akira Kamatsuka"
    },
    {
      "name": "Takahiro Yoshida"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54qxd4drgg305.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.07624",
  "fulltext_url": null,
  "id": "54qxd4drgg305",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.07624",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "3109|Statistical Mechanics and Entropy"
    ]
  ],
  "openalex": "W7160827531",
  "pdf_url": "https://arxiv.org/pdf/2605.07624",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54qxd4drgg305.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2605.07624",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.07624"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Statistical Mechanics and Entropy",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Kolmogorov--Nagumo Mean Frameworks for Conditional Entropy",
  "title_text": "Kolmogorov--Nagumo Mean Frameworks for Conditional Entropy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/54qxd4drgg305",
  "venue": "arXiv",
  "versions": []
}