{
  "abstract": "Let $(\\mathcal T_t)_{t\\geqslant0}$ be a quantum Markov semigroup on a von Neumann algebra and let $\\mathcal A$ be an invariant Feller $C^*$-algebra. We formulate the $e$-property on the full state space and show that its quantitative defect is equivalent, within an optimal factor two, to the Hausdorff measure of non-compactness of observable orbits. We develop Cesàro and Lip-norm criteria and a generalised Doeblin minorisation by a state-space contracting positive map, including finite-dimensional and measure-prepare factorisations. When every observable has the $e$-property, the Jacobs--de Leeuw--Glicksberg decomposition identifies the reversible Choi--Effros algebra and the norm-stable sector. Expected and decoherence-free subalgebras transfer the property under norm decay of the complementary dynamics, including infinite-dimensional ultracontractive and finite-index Pimsner--Popa regimes. Finally, we establish the full comparison hierarchy among ordinary, eventual, Cesàro and pointwise eventual equicontinuity notions, reinforced by matrix Jamison and homoclinic flow counterexamples. Projection-face criteria are treated in a companion paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00703",
  "author_total": 2,
  "authors": [
    {
      "name": "Tomasz Kania"
    },
    {
      "name": "Mariusz Niwiński"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fsr4mnv7kkrtg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00703",
  "fulltext_url": null,
  "id": "fsr4mnv7kkrtg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00703",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00703",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fsr4mnv7kkrtg.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00703",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00703"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The e-Property for Quantum Markov Semigroups",
  "title_text": "The e-Property for Quantum Markov Semigroups",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/fsr4mnv7kkrtg",
  "venue": "arXiv",
  "versions": []
}