Uploaded February 2020 | Updated September 2026, 3 weeks ago
Previously we've seen that our "colliding billiard balls" model for a monatomic gas has chaotic dynamics. Therefore, it is hopeless to try and describe the exact dynamical evolution of such a system. However, we can turn this to our advantage by treating the system as so unpredictable that it can be treated as a random process. Then, particular dynamical states can be characterized by their probability of occurrence. This is the basic idea of statistical mechanics. We begin with the derivation of the fundamental statistical formula we will need to analyze the statistics of a gas. We achieve this by analyzing the "toy" problems of flipping coins and distributing balls among boxes.
Previously we've seen that our "colliding billiard balls" model for a monatomic gas has chaotic dynamics. Therefore, it is hopeless to try and describe the exact dynamical evolution of such a system. However, we can turn this to our advantage by treating the system as so unpredictable that it can be treated as a random process. Then, particular dynamical states can be characterized by their probability of occurrence. This is the basic idea of statistical mechanics. We begin with the derivation of the fundamental statistical formula we will need to analyze the statistics of a gas. We achieve this by analyzing the "toy" problems of flipping coins and distributing balls among boxes.
