Information-Theoretic Typicality and Asymptotic Equipartition Property of Boltzmann’s Accessible Microstates

Abstract

The paper shows that, for large number of particles and for distinguishable and noninteracting identical particles, convergence to equiprobability of the W microstates of the famous Boltzmann-Planck entropy formula S = k log(W) is proved, in the thermodynamical limit, by the asymptotic equipartition property, a cornerstone of information theory. Specifically, the paper shows that the W accessible microstates appearing in the Boltzmann-Planck entropy formula are the elements of the information theoretic typical set. Typicality of accessible microstates, which has been already invoked in the past as a consequence of the weak law of large number, is discussed here for the first time in the information-theoretic perspective. This result further strengthens the link between information theory and statistical mechanics.