The Shannon-McMillan Theorem Proves Convergence to Equiprobability of Boltzmann's Microstates

TL;DR

This paper demonstrates that the Shannon-McMillan theorem can be used to prove the convergence to equiprobability of microstates in Boltzmann's entropy formula for large systems of distinguishable, non-interacting particles, strengthening the link between information theory and statistical mechanics.

Contribution

It provides a rigorous proof connecting the Shannon-McMillan theorem to the equiprobability of microstates in statistical mechanics.

Findings

Convergence to equiprobability is established for large particle systems.

The proof applies to distinguishable, non-interacting particles.

The result reinforces the connection between information theory and statistical mechanics.

Abstract

The paper shows that, for 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.