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  "slug": "tsallis-heat-order-classification",
  "title": "Complete monotonicity of Tsallis entropy under heat flow: a sharp order classification",
  "shortTitle": "Only one entropy order survives",
  "url": "https://evidencepress.org/releases/tsallis-heat-order-classification/",
  "oneLine": "The universal alternating-derivative hierarchy holds only at order two; the counterexample density may vary with the derivative being tested.",
  "abstract": "This AI-assisted unrefereed candidate classifies positive Tsallis orders for universal alternating heat derivatives. Only order two survives. An order-dependent spectral construction extends an inherited Gaussian-localization method; the Shannon counterexample and quadratic case are attributed. A separate order-13 rational witness is not claimed log-concave or least-order.",
  "datePublished": "2026-11-06",
  "dateModified": "2026-11-06",
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  "doi": "10.5281/zenodo.24001602",
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  "authors": [
    "Anonymous"
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      "note": "Public GitHub and Zenodo archives were downloaded in full and matched the frozen release assets; this verifies availability and byte identity, not independent scientific reproduction."
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    {
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      "question": "Does the producer’s own pipeline reproduce the stated result from the archived package?",
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  "metadataProvenance": "Prepared from final manuscript and bibliography on 6 November 2026. Final provider availability awaits canonical readback.",
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  "keywords": [
    "Tsallis entropy",
    "heat flow",
    "complete monotonicity",
    "Gaussian localization",
    "counterexample"
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    "Positive Tsallis orders admit the universal alternating heat-derivative hierarchy exactly at order two.",
    "For each fixed nonexceptional order, a smooth strictly log-concave counterexample family depends on sufficiently large derivative order.",
    "Separate order-3/2, derivative-13 witness at heat time 1/50 with rational certificate; no log-concavity or least-order claim.",
    "Elementary dilation permits variance or time normalization, not independent choice of both."
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  "relatedWorks": [
    {
      "citation": "Wu, Yu and Guo (2025). On the Complete Monotonicity of Rényi Entropy. IEEE Transactions on Information Theory.",
      "url": "https://doi.org/10.1109/TIT.2025.3561384",
      "doi": "10.1109/TIT.2025.3561384"
    },
    {
      "citation": "Gu and Sellke (2026). A Counterexample to the Gaussian Completely Monotone Conjecture.",
      "url": "https://doi.org/10.48550/arXiv.2605.11656",
      "doi": "10.48550/arXiv.2605.11656"
    },
    {
      "citation": "Zou, Fan, Gao and Wang (2026). An Explicit Family of Log-Concave Counterexamples to the Gaussian Completely Monotone Conjecture.",
      "url": "https://doi.org/10.48550/arXiv.2608.30275",
      "doi": "10.48550/arXiv.2608.30275"
    },
    {
      "citation": "Wu and Yu (2025). Entropic Isoperimetric and Cramér–Rao Inequalities for Rényi–Fisher Information.",
      "url": "https://doi.org/10.48550/arXiv.2504.01837",
      "doi": "10.48550/arXiv.2504.01837"
    },
    {
      "citation": "Sun (2026). Concavity of Tsallis Entropy and Tsallis Entropy Power along Heat Flow.",
      "url": "https://doi.org/10.48550/arXiv.2601.12944",
      "doi": "10.48550/arXiv.2601.12944"
    }
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