{
  "abstract": "We consider a closed macroscopic quantum system in a pure state $ψ$ evolving unitarily with Hamiltonian $H$ in a finite-dimensional Hilbert space $\\mathscr{H}$. Following von Neumann, we assume a decomposition of $\\mathscr{H}$ into mutually orthogonal subspaces $\\mathscr{H}_ν$, where each $ν$ represents a macro state, and $\\mathscr{H}_ν$ contains the pure states compatible with $ν$. We define the quantum Boltzmann entropy for a macro state $ν$ as $S_\\mathrm{qB}(ν) = k_{\\mathrm{B}} \\log \\dim \\mathscr{H}_ν$, where $k_\\mathrm{B}$ is the Boltzmann constant. Goldstein et al. [http://arxiv.org/abs/1903.11870] have suggested, as a version of the second law of thermodynamics, that $S_\\mathrm{qB}$ predominantly increases with time for realistic macroscopic systems. Here, we discuss precise versions of this statement and confirm them for several simple models of $H$ and $\\mathscr{H}_ν$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18553",
  "author_total": 2,
  "authors": [
    {
      "name": "Cedric Igelspacher"
    },
    {
      "name": "Roderich Tumulka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6dp0va5s0n3wc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18553",
  "fulltext_url": null,
  "id": "6dp0va5s0n3wc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18553",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221769085",
  "pdf_url": "https://arxiv.org/pdf/2610.18553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6dp0va5s0n3wc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.18553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18553"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On the Increase of Boltzmann Entropy in Closed Macroscopic Quantum Systems",
  "title_text": "On the Increase of Boltzmann Entropy in Closed Macroscopic Quantum Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/6dp0va5s0n3wc",
  "venue": "arXiv",
  "versions": []
}