{
  "abstract": "We derive sharp lower bounds on the energy cost of Page-like entanglement entropy excursions in two-dimensional conformal field theory. For states satisfying the primary quantum null energy condition (QNEC), the positive null energy $E_+$ obeys a sharp lower bound with two branches separated by the threshold $ΔS=(c/6)\\ln 2$. We also derive a sharp lower bound on the net energy $E_{\\rm net}$, with a coefficient larger by a factor of two than the value quoted by Abdolrahimi and Page [Phys. Rev. D 92, 083005 (2015)] and, in the QNEC-saturating sector, we obtain a sharp lower bound on the negative energy $E_-$. The constants are sharp as infima over smooth conformal vacua. We determine the entropy profiles that minimize $E_+$ for general QNEC states and the one that minimizes $E_-$ in the saturating sector. Finally, for an excursion containing an infinite sequence of small sub-excursions within a finite duration, we derive a necessary condition for the total positive energy to remain finite, which is stronger than requiring the entropy to have finite total variation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03576",
  "author_total": 2,
  "authors": [
    {
      "name": "Soufiane Karmoudi"
    },
    {
      "name": "Mohammed Daoud"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/508a18qy2z200.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03576",
  "fulltext_url": null,
  "id": "508a18qy2z200",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03576",
  "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": "W7220417217",
  "pdf_url": "https://arxiv.org/pdf/2610.03576",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/508a18qy2z200.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.03576",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03576"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Sharp null-energy lower bounds for Page-like entropy excursions in two-dimensional conformal field theory",
  "title_text": "Sharp null-energy lower bounds for Page-like entropy excursions in two-dimensional conformal field theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/508a18qy2z200",
  "venue": "arXiv",
  "versions": []
}