{
  "abstract": "In this note, we prove that every primitive KMS-symmetric quantum Markov semigroup on a finite-dimensional matrix algebra satisfies a modified logarithmic Sobolev inequality (MLSI). We also construct a primitive quantum Markov semigroup without KMS symmetry that fails MLSI, and a primitive KMS-symmetric quantum Markov semigroup that fails complete MLSI (CMLSI). The latter construction also provides a non-primitive KMS-symmetric quantum Markov semigroup without MLSI. For the graph-based KMS-symmetric quantum Markov semigroups studied here, we prove MLSI and CMLSI when the underlying graph is connected and has at least three vertices. Finally, we establish CMLSI for a class of primitive bimodule KMS-symmetric quantum Markov semigroups arising from fermionic systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13726",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhengwei Liu"
    },
    {
      "name": "Jincheng Wan"
    },
    {
      "name": "Jinsong Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fgdns7gfxhhp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13726",
  "fulltext_url": null,
  "id": "2fgdns7gfxhhp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13726",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.13726",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fgdns7gfxhhp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13726",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13726"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Some entropic inequalities for primitive KMS symmetric quantum Markov semigroups",
  "title_text": "Some entropic inequalities for primitive KMS symmetric quantum Markov semigroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2fgdns7gfxhhp",
  "venue": "arXiv",
  "versions": []
}