{
  "abstract": "Positive Wigner functions can have less Shannon entropy than the vacuum, even arbitrarily close to the vacuum state. We construct physical counterexamples and identify the competition that controls their entropy: the relative entropy to the vacuum phase-space density can exceed twice the mean photon number. A two-level family exhibits a finite window in which coherence lowers entropy while preserving global Wigner positivity. A complementary construction repairs a remote negative tail with an exponentially small thermal admixture; an explicit mixing weight of $2\\times10^{-21}$ preserves a rigorously established entropy decrease. Optimisation over all one-mode Wigner-nonnegative states gives the sharp low-energy scale $E^γ/[\\ln(1/E)]^β$, with $γ\\simeq0.7412$ and $β\\simeq0.5861$. Because $γ<1$, tensor products can have vanishing total energy and trace distance from vacuum while their entropy deficit diverges. We derive the exact half-transmission threshold for universal Shannon-entropy recovery and connect it to companion results showing residual non-Gaussian structure. The counterexamples reveal distinct controls on entropy: coherence sets the local descent, mode number amplifies it, and loss restores the vacuum bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13312",
  "author_total": 1,
  "authors": [
    {
      "name": "Zixuan He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d0xfyk5szt2hz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13312",
  "fulltext_url": null,
  "id": "d0xfyk5szt2hz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13312",
  "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 Mechanics and Applications"
    ]
  ],
  "openalex": "W7213312420",
  "pdf_url": "https://arxiv.org/pdf/2609.13312",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d0xfyk5szt2hz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.13312",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13312"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Wigner entropy below vacuum: physical counterexamples and stability limits",
  "title_text": "Wigner entropy below vacuum: physical counterexamples and stability limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/d0xfyk5szt2hz",
  "venue": "arXiv",
  "versions": []
}