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air.unimi.it (University of Milan repository) and the "Boltzmann-Jeans conjecture" literature, 2026-10-08

Investigator run 1, Jeans-JH. Found by the Chrome Google queries "Jeans" 1903 OR 1904 vibrational energy transfer collision exponential adiabatic "Landau-Teller" history and "Boltzmann-Jeans conjecture" Galgani Benettin arXiv. Priority 2 (later independent theory that supports and extends the inventor's point) for claims 1-2.

Document obtained

G. Benettin, A. Carati, G. Gallavotti, "A rigorous implementation of the Jeans-Landau-Teller approximation for adiabatic invariants" (preprint dated 26 April 1995, 21 pp.). URL: https://air.unimi.it/retrieve/dfa8b995-4270-748b-e053-3a05fe0a3a96/bcg_xieta.pdf. Saved as files/benettin-carati-gallavotti-1995-jeans-landau-teller.pdf. [web]

What it says (paraphrase, short quotes)

  • Abstract: rigorous bounds on the rate of energy exchange between vibrational and translational degrees of freedom are proved for simple classical models of diatomic molecules, "in agreement with an elementary approximation introduced by Landau and Teller". The method is perturbation theory "beyond all orders".
  • Introduction: models like their eq. (1.1), a diatomic molecule colliding with a wall or a point mass, "have been introduced by Jeans [J1, J2]" to study relaxation times in polyatomic gases and why vibrations of diatomic gases do not take part in energy exchange. The authors write that it is "not well known" that Jeans conjectured, after Boltzmann, that the apparent "freezing" of fast vibrations comes from energy exchanges too small to matter on a reasonable time scale. Jeans proposed an exponential law of the form Delta E ~ E exp(-omega tau) (their eq. 1.2).
  • References: [J1] Jeans, Phil. Mag. 6, 279 (1903); [J2] Jeans, Phil. Mag. 10, 91 (1905); [Bo1] Boltzmann, Nature 51, 413 (1895); [Bo2] Boltzmann, Lectures on Gas Theory, Part II §45; [LT] Landau and Teller, Physik. Z. Sowjetunion 10, 34 (1936); [Be1] Benettin, "On the Boltzmann-Jeans Conjecture for a Classical 'Freezing' of Fast Degrees of Freedom", Taormina 1991 proceedings (1992); [BGG1] Benettin, Galgani, Giorgilli, "The dynamical foundation of classical statistical mechanics and the Boltzmann-Jeans conjecture" (Birkhauser 1993); [C] A. Carati, PhD thesis "Il metodo di Jeans-Landau-Teller per lo studio degli invarianti adiabatici".
  • Benettin, Galgani, Giorgilli, Comm. Math. Phys. 121, 557 (1989), cited by later arXiv papers as the basis of the "Boltzmann-Jeans conjecture" [web, snippet].
  • Relaxation time "increase[s] as the exponential of the square root of the energy of excitation, in agreement with the Boltzmann-Jeans conjecture" (ResearchGate item "Relaxation, the Boltzmann-Jeans Conjecture and Chaos") [web, snippet].
  • arXiv:1003.3710 (2010), "Slow relaxation to equipartition in spring-chain systems"; cond-mat/0203430 (Nakagawa 2002, "logarithmically slow relaxation... called Boltzmann-Jeans conjecture"); arXiv:2209.02210 (Yamaguchi 2022) [web, snippets].
  • E. E. Nikitin, "70 years of Landau-Teller theory for collisional energy transfer", PCCP 2008 (RSC) [web, snippet].
  • E. Legnaro (Thessaloniki thesis 2023, and arXiv 2023) traces the "original idea found back in (Jeans, 1903) and (Jeans, 1905)" [web, snippet].
  • Contopoulos and Voglis (eds.), Galaxies and Chaos (Springer LNP 2003), a chapter on the Landau-Teller model that cites Jeans "with the explicit aim of avoiding a recourse to quantization" [web, snippet; PDF at prl.res.in not opened].

Bearing on the claims

  • Claim 2 (slow feeding via exp(-2 p beta)): mathematical physicists since about 1989 have named the idea after Jeans (with Boltzmann) as the "Boltzmann-Jeans conjecture", and have proved rigorous versions of the exponentially slow energy exchange for model systems. The Milan-Padua school calls the approximation "Jeans-Landau-Teller". This is independent later theory that supports the mechanism Jeans proposed as a classical dynamical fact about time scales.
  • What it does not do: it does not say that equilibrium specific heats are classical. The mainstream account of equilibrium heat capacities remains quantum freeze-out (see claims.md). Galgani and co-workers have, in other papers, explored how far classical metastability could go toward Planck's law [memory, medium; not checked this run]. That is a lead for the contrarian and physicist reviewers.
  • Interested parties: none commercial; academic authors.