The Shannon–McMillan Theorem Proves Convergence to Equiprobability of Boltzmann’s Microstates

Abstract

This paper shows that, for a large number of particles and for distinguishable and non-interacting identical particles, convergence to equiprobability of the W microstates of the famous Boltzmann–Planck entropy formula S = k log(W) is proved by the Shannon–McMillan theorem, a cornerstone of information theory. This result further strengthens the link between information theory and statistical mechanics.

Keywords

• Boltzmann–Planck entropy formula
• Shannon–McMillan theorem
• equiprobability of microstates