Counterexamples of Boltzmann's equation

TL;DR

This paper demonstrates that certain simple setups cannot be accurately modeled by Boltzmann's equation and introduces a path-integral approach as an alternative method for kinetic theory analysis.

Contribution

The paper identifies limitations of Boltzmann's equation in specific scenarios and proposes a new path-integral approach for better modeling.

Findings

Simple setups cannot be treated by Boltzmann's equation

Path-integral approach yields verifiable results

Highlights limitations of traditional kinetic theories

Abstract

To 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.