Is the Information Entropy the Same as the Statistical Mechanical Entropy?

TL;DR

This paper demonstrates that Shannon's information entropy formula is only valid for specific states, and a more general entropy expression is necessary for statistical mechanics, including an additional term.

Contribution

It derives a general entropy formula for statistical mechanics, extending Shannon's original expression by including an extra term for broader applicability.

Findings

Shannon's entropy applies only to specific state sets.

A new entropy formula includes an additional term.

The derivation clarifies the relationship between information and statistical mechanical entropy.

Abstract

It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the expression for the entropy as a function of the probability. A simple derivation of the general formula is given.