{
  "abstract": "We show that the Boltzmann-Grad (BG) limit, $N\\varepsilon^{d-1}=α=\\text{const}$, is not a neutral scaling condition but already encodes the Second Law of Thermodynamics, resolving Loschmidt's paradox. Newton's First Law is the bridge: applying the BG condition locally to two adjacent cells at different temperatures, we decompose their evolution into a free-streaming period $δt_f$, governed by inertia alone, during which molecules cross the interface ballistically and still carry their cell of origin's velocity distribution; and a collisional adjustment period $δt_a$, governed by Newton's Second Law, during which the locally mixed, non-Gaussian population relaxes toward a new Gaussian equilibrium. Using the one-dimensional Gaussian velocity distribution, we show that isotropy alone produces non-zero net molecular and momentum flux across the interface, directed from the warmer to the cooler cell -- the microscopic origin of the pressure gradient driving the system toward uniformity. Treating relaxation as a sum of random collisional increments, the Central Limit Theorem fixes the collision count $n^*$ required for convergence, giving $δt_a \\sim n^*\\,\\ell/\\bar v$. This decomposition resolves Loschmidt's paradox: his reversal acts on a fixed, identifiable set of molecules, while the temperature field Boltzmann's equation tracks is carried by an ever-changing local population; the step relating the two -- convergence under the Central Limit Theorem -- is itself a coarse-graining that discards microscopic information by construction, recoverable only at an unavoidable thermodynamic cost, by Landauer's principle. Temporal irreversibility is present from the moment the BG framework, and the coarse-graining it requires, are adopted -- not generated during derivation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25056",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhaohua Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4chavgvek53b5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25056",
  "fulltext_url": null,
  "id": "4chavgvek53b5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25056",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7204464364",
  "pdf_url": "https://arxiv.org/pdf/2608.25056",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4chavgvek53b5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2608.25056",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25056"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "The Hidden Second Law of Thermodynamics behind the Boltzmann-Grad Limit",
  "title_text": "The Hidden Second Law of Thermodynamics behind the Boltzmann-Grad Limit",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/4chavgvek53b5",
  "venue": "arXiv",
  "versions": []
}