From billiards to thermodynamic laws: I. Stochastic energy exchange model

TL;DR

This paper introduces a stochastic energy exchange model derived from a billiards-like microscopic heat conduction system, demonstrating its ability to preserve key properties such as ergodicity and thermal conductivity through numerical analysis.

Contribution

The paper presents a novel stochastic energy exchange model that accurately captures the dynamics and properties of a microscopic billiard-like heat conduction system.

Findings

The stochastic model preserves ergodicity of the original system.

The model maintains the thermal conductivity properties.

Numerical results validate the model's accuracy.

Abstract

This paper studies a billiards-like microscopic heat conduction model, which describes the dynamics of gas molecules in a long tube with thermalized boundary. We numerically investigate the law of energy exchange between adjacent cells. A stochastic energy exchange model that preserves these properties is then derived. We further numerically justified that the stochastic energy exchange model preserves the ergodicity and the thermal conductivity of the original billiard model.