Non-equilibrium statistical mechanics: a solvable model

TL;DR

This paper introduces a simple two-temperature spin model that exemplifies key concepts of non-equilibrium statistical mechanics, providing accessible insights and solutions for educational and computational purposes.

Contribution

The paper presents a solvable two-temperature spin model that captures essential non-equilibrium features and is suitable for educational use and benchmarking.

Findings

Provides explicit steady state solutions for the model

Demonstrates full time dependence of configuration probabilities for small systems

Serves as an accessible tool for teaching and validating non-equilibrium models

Abstract

A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models but that allows straightforward steady state solutions and, for small systems, development of the full time dependence for configuration probabilities. The model is easily accessible to upper-level undergraduate students, and also provides a good check for computer models of larger systems.