{
  "abstract": "For positive semidefinite matrices $A,B$ and $1/2\\leα\\le1$, we establish $\\operatorname{Tr}\\!\\left[A\\,D\\log(A^α+B^α)(B^α)\\right] \\le s^s(1-s)^{1-s}\\operatorname{Tr}[A^αB^{1-α}]$, where $s=(1-α)/α$, with the optimal coefficient. The proof uses a superoperator representation of the directional derivative of the logarithm and an Araki-type estimate for the derivative of a fractional power. Both this inequality and its symmetric-quotient counterpart extend to positive trace-class $A$ and positive, possibly unbounded, self-adjoint $B$ on a separable Hilbert space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39598",
  "author_total": 2,
  "authors": [
    {
      "name": "Hao-Chung Cheng"
    },
    {
      "name": "Po-Chieh Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2rvbnrja425v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39598",
  "fulltext_url": null,
  "id": "b2rvbnrja425v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39598",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39598",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2rvbnrja425v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39598",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39598"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sharp Tilting Inequalities",
  "title_text": "Sharp Tilting Inequalities",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/b2rvbnrja425v",
  "venue": "arXiv",
  "versions": []
}