2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/124785To test kinetic theories, simple and practical setups are proposed. It turns out that these setups cannot be treated by Boltzmann's equation. An alternative method, called the path-integral approach, is then employed and a number of ready-for-verification results are obtained.17 pages, 6 figures, theoretical analyses have been moved to appendixesStatistical MechanicsCounterexamples of Boltzmann's equationtext