Gibbs Paradox in the View of Information Entropy

TL;DR

This paper applies information theory to analyze the Gibbs Paradox, showing that indistinguishability is unnecessary and that mixing entropy is independent of molecular types, challenging traditional views.

Contribution

It introduces an information-theoretic perspective to resolve Gibbs Paradox and clarifies the role of molecular distinguishability in entropy calculations.

Findings

Indistinguishability is not needed to resolve the paradox.

Mixing entropy is independent of molecular types.

The actual mixing entropy is smaller than traditionally thought.

Abstract

This paper introduces the basic concepts of information theory. Based on these concepts, we regard the states in the state space and the types of ideal gases as the symbols in a symbol set to calculate the mixing entropy of ideal gas involved in Gibbs Paradox. The discussion above reveals that the non-need for distinguishing can resolve the contradiction of Gibbs Paradox, implying the introduction of indistinguishability is not necessary. Further analysis shows that the information entropy of gas molecular types does not directly correlate to the energy of a gas system, so it should not be used for calculating thermodynamic and statistical dynamic entropies. Therefore, the mixing entropy of the ideal gas is independent of the molecular types and is much smaller than the value commonly thought.