{
  "abstract": "We develop a semigroup interpolation method for sharp logarithmic Sobolev inequalities using spectral calculus and estimates of $\\mathrm{Re}\\langle\\,Lx,x^2\\rangle_2$, where $L$ generates an auxiliary symmetric quantum Markov semigroup. We apply the method to free groups and to crossed products of a finite von Neumann algebra $\\mathcal N$ by $\\mathbb Z$ or $\\mathbb Z_n$, for $n=2$ or $n\\ge4$, when the action commutes with the semigroup on $\\mathcal N$. In particular, the word-length generators on quantum tori and the Weyl word-length generators on $M_n(\\mathbb C)$ satisfy logarithmic Sobolev inequalities with optimal constant $2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25180",
  "author_total": 1,
  "authors": [
    {
      "name": "Gan Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4cpv374xnjacc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25180",
  "fulltext_url": null,
  "id": "4cpv374xnjacc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25180",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223066627",
  "pdf_url": "https://arxiv.org/pdf/2610.25180",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4cpv374xnjacc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25180",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25180"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharp quantum logarithmic Sobolev inequalities via semigroup interpolation",
  "title_text": "Sharp quantum logarithmic Sobolev inequalities via semigroup interpolation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4cpv374xnjacc",
  "venue": "arXiv",
  "versions": []
}