{
  "abstract": "The celebrated Evans--Searles, respectively Gallavotti--Cohen, fluctuation theorem concerns certain universal statistical features of the entropy production rate of a classical system in a transient, respectively steady, state. In this paper, we review and compare several possible extensions of these fluctuation theorems to quantum systems. We present, in an introductory way, the approach proposed in a recent series of works [Lett. Math. Phys. 114, 32 (2024): doi:10.1007/s11005-024-01777-0], [Rev. Math. Phys 38, 2461006 (2026): doi:10.1142/S0129055X24610063], [Commun. Math. Phys. 406, 201 (2025): 10.1007/s00220-025-05360-z] and [J. Math. Phys. 67, 022101 (2026): doi:10.1063/5.0311182] including a previously missing extension of the Gallavotti--Cohen (steady state) version of the FT to two-time measurement entropy production in the algebraic setting of quantum dynamical systems. We focus on the open quantum systems, where a small system interacts with several (infinitely extended) reservoirs, and discuss the following approaches: naive, two-time measurement, phase space contraction and ancilla state tomography. We review the connection with modular theory. The latter provides a way to extend the classical notions to the quantum domain. We discuss the quantum version of the principle of regular entropic fluctuations, introduced in the classical context in [Nonlinearity 24, 699 (2011): doi:10.1088/0951-7715/24/3/003]. Finally, we relate the statistical properties of these various notions of entropy production to spectral resonances of quantum transfer operators and apply this approach to a paradigmatic model of non-equilibrium statistical mechanics: the spin-fermion model. The results presented here shed a new light on the nature of entropic fluctuations in quantum statistical mechanics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40463",
  "author_total": 5,
  "authors": [
    {
      "name": "Tristan Benoist"
    },
    {
      "name": "Laurent Bruneau"
    },
    {
      "name": "Vojkan Jakšić"
    },
    {
      "name": "Aannalisa Panati"
    },
    {
      "name": "Claude-Alain Pillet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ayc9jx7wexw8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40463",
  "fulltext_url": null,
  "id": "ayc9jx7wexw8z",
  "issns": [],
  "landing_url": "https://hal.science/hal-05845019v1",
  "language": "en",
  "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.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
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      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.phys.mphy"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40463",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ayc9jx7wexw8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:03Z",
      "native_id": "hal-05845019",
      "source": "hal",
      "url": "https://hal.science/hal-05845019v1"
    },
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40463",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40463"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Entropic Fluctuations in Quantum Statistical Mechanics: A Review",
  "title_text": "Entropic Fluctuations in Quantum Statistical Mechanics: A Review",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/ayc9jx7wexw8z",
  "venue": "HAL",
  "versions": []
}