Kuzovlev Yu.E.
Molecular Brownian motion and falsity of the ``law of large numbers''
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ABSTRACT. Real thermal motion of gas particles, free electrons, etc., at long time intervals (much greater than mean free-flight time) possesses, contrary to its popular mathematical models, essentially non-Gaussian statistics, thus implying that chaotic path of a molecular Brownian particle can not be separated into ``statistically independent'' constituent parts and so the ``law of large numbers'' is not applicable, even under the Boltzmann-Grad limit. A simple proof of this statement is suggested basing on only the determinism and reversibility of microscopic dynamics and besides incidentally derived virial expansion of the path probability distribution.