You learn the contents in this section in the standard statistical mechanics courses. However, as I had no chance to use this knowledge in my own research, I forgot some of its details, and had to refresh my memories to write these articles. Nevertheless, articles here are very important if you will specialize in statistical mechanics or condensed matter physics. However, if I remember correctly, my statistical mechanics courses skipped the material covered in “The chemical equilibrium.” I first learned a consequence of the conclusion in that article when I studied chemistry, but I had no idea why such a chemical law should be obeyed. Now, I know from my self-study of the material from statistical mechanics textbooks. “The chemical equilibrium” is important later when we talk about the thermal history of early universe.