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

Source: [Hard-ball gas as hard nut of statistical mechanics (why mathematicians missed 1/f-noise there)](<https://www.sota2.com/research/paper/68fa2dd51e209131ce85ccf2>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:30:28.814Z

Authors: Yu.E.Kuzovlev

Published: 2014-11-12T17:53:58.000Z

## 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

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1411.3261>)

[PDF](<https://arxiv.org/pdf/1411.3261.pdf>)