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arXiv · 1411.3261

Hard-ball gas as hard nut of statistical mechanics (why mathematicians missed 1/f-noise there)

Yu. E. Kuzovlev
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Abstract

We continue discussion of hard-ball models of statistical mechanics, by example of random walk of hard ball immersed into equlibrium ideal gas. Our goal is to highlight decisive role of specific phase-space subsets, despite their vanishingly smaall Lebesgue measures under the Boltzmann-Grad limit. The "art of draining" such subsets in conventional mathematical constructions resulted in loss of so principal property of many-particle systems as 1/f-noise in diffusivities, mobilities and other transport and relaxation rates. We suggest new approaches to formulation and analysis of evolution equations for hierarchy of probability distribution functions of infinite hard-ball systems, thus further overcoming prejudices of Boltzmannian kinetics and mistakes of its modern adepts

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Yu. E. Kuzovlev. 2014-11-12. Hard-ball gas as hard nut of statistical mechanics (why mathematicians missed 1/f-noise there). https://arxiv.org/abs/1411.3261

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