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.

中文翻译：

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用格子模型说明熵，自由能和热力学平衡的概念

在本文中，我们使用简单的晶格模型从微观角度说明熵，自由能和热力学平衡的概念。这些物理概念基于离散概率分布和加权平均值的基本知识。关于该模型的计算涉及基本的代数和计数，这将帮助学生从一个具体的例子中获得重要的见识。需要更高级的数学以完全理解一些详细的推导，这些推导可以用作该主题的可选教材。