{
  "abstract": "It is shown that Shannon entropy, Fisher information, and quantum-mechanical kinetic energy may all be viewed as measures of correlation. We begin with a fundamental correlation-destroying map: a joint probability density $ρ(x,y)$ is replaced by $ρ_x(x)ρ_y(y)$, the product of its marginal distributions. In the discrete case, Shannon's entropy is nondecreasing under this map. For continuous distributions, this fundamental map leads to a well-behaved, coordinate-invariant correlation measure, analogous to the discrete Shannon entropy: \\[ I[ρ] = h[ρ_x] + h[ρ_y] - h[ρ]. \\] In the continuous case, however, another measure appears: Fisher information. The relative Fisher information $J(ρ\\|ρ_xρ_y)$ behaves similarly under the fundamental map. For a normalized real quantum wavefunction, this decrease is exactly proportional to the decrease in mean kinetic energy, \\[ \\langle T\\rangle_ψ- \\langle T\\rangle_Φ= \\frac{\\hbar^2}{8m} J(ρ\\|ρ_xρ_y), \\qquad Φ= \\sqrt{ρ_x ρ_y}. \\] In Jaynes's language, the result supports a principle of minimum justified correlation: given physical constraints and a set of possible distributions or related amplitudes satisfying those constraints, select from that set those with the least correlation. This is Part I of a two-part paper. Here we develop the entropy, Fisher-information, and kinetic-energy identities above, and state the principle they support. Part II addresses questions which Part I raises but leaves unanswered: multiple solutions, time dependence, the role of spin, a route to the Schrödinger equation itself, and a proposed experimental test. AI has been used.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38124",
  "author_total": 1,
  "authors": [
    {
      "name": "John H Van Drie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0470jyms9h82b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38124",
  "fulltext_url": null,
  "id": "0470jyms9h82b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38124",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7214885547",
  "pdf_url": "https://arxiv.org/pdf/2609.38124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0470jyms9h82b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.38124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38124"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The Principle of Minimum Justified Correlation",
  "title_text": "The Principle of Minimum Justified Correlation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/0470jyms9h82b",
  "venue": "arXiv",
  "versions": []
}