Classical Resolution of the Gibbs Paradox from the Equal Probability Principle: An Informational Perspective

TL;DR

This paper offers a classical, information-based resolution to the Gibbs paradox, avoiding quantum assumptions and emphasizing entropy as a measure of ignorance, thereby linking information theory with thermodynamics.

Contribution

It introduces a purely classical, informational approach to resolving the Gibbs paradox without using quantum indistinguishability or the 1/N! correction.

Findings

Gibbs entropy can be interpreted as Shannon entropy of ignorance

The resolution is achieved within classical ensemble theory

Clarifies the link between information and work in gas mixing

Abstract

The Gibbs paradox is a conventional paradox in classical statistical mechanics, typically resolved by invoking quantum indistinguishability through the 1/N! correction. In this letter, we present a resolution within classical ensemble theory, which relies solely on the equal probability principle and does not invoke the 1/N! correction. Our resolution can be naturally interpretated from a purely informational perspective, where the Gibbs entropy is explicitly regarded as the Shannon entropy, quantifying ignorance rather than disorder. From this informational perspective, we also clarify the connection between information and extractable work in the gas mixing processes. Our work opens a new avenue to reconsider the role of information in statistical mechanics.