{
  "abstract": "The modular Hamiltonian plays an important role in quantum information theory, quantum field theory, and the AdS/CFT correspondence. In this paper, we study a specific dynamical setup: starting from the tensor product of the reduced density matrices of a reference state, we evolve this product state under the modular flow generated by the reference state itself. We then investigate the resulting change in the entanglement entropy of a given region, which we call the modular entanglement shift (MES). Unlike evolution under a fixed quantum channel, this modular evolution obeys no general principle requiring the MES to have a definite sign. For a bipartition into subsystems A and B, we establish an exact entropy balance: the sum of the MESs for A and B equals the mutual information generated along the orbit. Consequently, their sum is nonnegative, even though either individual shift may be negative. For two disjoint intervals in the vacuum of a two-dimensional conformal field theory, however, we prove that a global conformal involution exchanging the intervals forces the two MESs to be equal. It follows that each MES is nonnegative along the modular flow. We establish this result both using a conformally transported regulator and intrinsically in terms of Araki relative entropy. Finally, we identify the modular-flow orbit with a Connes cocycle orbit and discuss possible applications to the AdS/CFT correspondence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29329",
  "author_total": 1,
  "authors": [
    {
      "name": "Liangyu Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70376xh69ap86.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29329",
  "fulltext_url": null,
  "id": "70376xh69ap86",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29329",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7204879434",
  "pdf_url": "https://arxiv.org/pdf/2608.29329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70376xh69ap86.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.29329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29329"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Inequalities and Positivity in Modular Flowed Entanglement Entropy",
  "title_text": "Inequalities and Positivity in Modular Flowed Entanglement Entropy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/70376xh69ap86",
  "venue": "arXiv",
  "versions": []
}