{
  "abstract": "In this paper, we study finite-mode Gaussian quantum Markov semigroups with a faithful invariant Gaussian state. We present an algebraic characterization of the complete modified logarithmic Sobolev inequality relative to the fixed-point algebra, and we obtain the corresponding optimal constant under the assumption that the drift evolution $e^{t\\mathbf{Z}}$ converges as $t\\to\\infty$. We establish hypercontractivity for such quantum Markov semigroups with Hurwitz drift, in the sense that every fixed pair $1<p<q<\\infty$ is attained at sufficiently large times. We find that the usual reverse hypercontractive curves with a positive rate from time zero can fail in general, but every fixed pair $1/2 < p < q < 1$ is attained at sufficiently large times under the Hurwitz assumption. We also systematically investigate the $p$-logarithmic Sobolev inequality and show that the $p$-logarithmic Sobolev constant can be negative for $0 < p < 1/2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06201",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhengwei Liu"
    },
    {
      "name": "Jincheng Wan"
    },
    {
      "name": "Jinsong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0tthk9nzqzfjd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06201",
  "fulltext_url": null,
  "id": "0tthk9nzqzfjd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06201",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7220700992",
  "pdf_url": "https://arxiv.org/pdf/2610.06201",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0tthk9nzqzfjd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06201",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06201"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Entropy Contraction and Hypercontractivity for Gaussian Quantum Markov Semigroups",
  "title_text": "Entropy Contraction and Hypercontractivity for Gaussian Quantum Markov Semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/0tthk9nzqzfjd",
  "venue": "arXiv",
  "versions": []
}