## The Ergodic Theorem

Introduction Suppose you want to model the dynamics of a gas inside a box. We model the gas as a bunch of molecules, which can hit each other and the box they are enclosed in. We consider the situation in which there is no loss of energy (elastic collisions, friction, heat, etc.). We can write physical equations of motions to model this gas. The problem is that the number of balls is enormous, and we cannot describe the position and momentum of each particle....