Ehrenfest model of diffusion

The Ehrenfest model of diffusion, developed by physicist Paul Ehrenfest, is a mathematical model used to illustrate the statistical interpretation of the second law of thermodynamics. It visualizes a system of N gas molecules in a container divided into two parts. At each step, a randomly chosen molecule moves to the other side. The model tracks the number of molecules on one side, X(t), as a stochastic process.1

While the second law suggests entropy only increases, the Ehrenfest model shows that random fluctuations can lead to temporary decreases in entropy, even a return to the initial state. However, the time required for such an observable decrease is astronomically long, making the second law hold true on a macroscopic, experimental scale.1