Thermal Physics from Combinatorics

From the 1850s to the 1930s, through the advent of quantum mechanics, our understanding of thermodynamics underwent a revolution. Central to this revolution was our understanding of entropy -- at first thought to be a mysterious substance, then understood to simply be a count of the number of configurations a system can find itself in. The field of statistical physics was born, which demonstrated that the law of large numbers familiar from statistics had massive predictive power in our study of the world around us. In this Semilab, we will understand what entropy truly is, how to compute it using combinatorial techniques, and understand its relationship to temperature and other measurable quantities. We will also learn how diagrammatic techniques, due to Feynman, helped simplify tedious calculations by drawing pretty pictures instead.