2014/11/12 by Kuzovlev, Yu. E.
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1411.3261
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