{
  "abstract": "In this work, we develop a general framework for deriving the first law of black hole thermodynamics and the associated Smarr-type relation for 4-dimensional static spherically symmetric spacetimes within a broad class of generalized entropy models. In addition, by employing the entropy representation for the Reissner--Nordström (RN) black hole, we determine a concise curvature functional that depends only on this representation and its derivatives. A general flatness condition is derived, demonstrating that when the entropy Hessian metric is regular and nondegenerate, both homogeneous power-law transformations and a separate logarithmic branch leave the RN black hole's Ruppeiner geometry flat. On the other hand, Rényi, Sharma-Mittal, Kaniadakis, and LQG-inspired entropy deformations typically give rise to nonvanishing curvature in the regular thermodynamic regime, demonstrating that the extremality of the RN black hole does not by itself require a curvature divergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.00381",
  "author_total": 3,
  "authors": [
    {
      "name": "Usman Zafar"
    },
    {
      "name": "Krishnakanta Bhattacharya"
    },
    {
      "name": "Kazuharu Bamba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cgxtcxn1xdyb8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.00381",
  "fulltext_url": null,
  "id": "cgxtcxn1xdyb8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.00381",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7160165601",
  "pdf_url": "https://arxiv.org/pdf/2605.00381",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cgxtcxn1xdyb8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2605.00381",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.00381"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Generalized First Law and Smarr-type Relation: Beyond Additivity and Extensivity",
  "title_text": "Generalized First Law and Smarr-type Relation: Beyond Additivity and Extensivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/cgxtcxn1xdyb8",
  "venue": "arXiv",
  "versions": []
}