This is the third of five guest videos while I’m on leave. It comes from a previous winner of the Summer of Math Exposition, Vilas Winstein, currently doing his PhD at Berkeley. In it, he covers some of the fundamental ideas in statistical mechanics, including defining temperature, entropy, and deriving the Boltzmann law, all in the service of creating a simplified and discretized model mirroring the behavior of a fluid transitioning between a liquid and gaseous state. Enjoy!