Illustrating the Concepts of Entropy, Free Energy, and Thermodynamic Equilibrium with a Lattice Model

In this article, we use a simple lattice model to illustrate the concepts of entropy, free energy, and thermodynamic equilibrium from a microscopic perspective. These physical concepts are based on elementary knowledge of discrete probability distribution and weighted average. Calculations about this model involve basic algebra and counting, which shall help students gain important insights from a concrete example. More advanced mathematics is needed to fully understand some detailed derivations that can serve as optional teaching materials for the topic.