Gibbs Paradox and Similarity Principle

TL;DR

This paper resolves the Gibbs paradox by showing that ideal mixtures have zero entropy change and introduces a similarity principle where higher component similarity increases entropy and stability across various systems.

Contribution

It provides a novel thermodynamic and information-theoretic explanation of the Gibbs paradox and formulates a similarity principle linking component similarity to entropy and stability.

Findings

Ideal mixtures have zero entropy change during formation.

Higher similarity among components increases entropy and stability.

Introduces a third law of information theory for perfect symmetry structures.

Abstract

As no heat effect and mechanical work are observed, we have a simple experimental resolution of the Gibbs paradox: both the thermodynamic entropy of mixing and the Gibbs free energy change are zero during the formation of any ideal mixtures. Information loss is the driving force of these spontaneous processes. Information is defined as the amount of the compressed data. Information losses due to dynamic motion and static symmetric structure formation are defined as two kinds of entropies - dynamic entropy and static entropy, respectively. There are three laws of information theory, where the first and the second laws are analogs of the two thermodynamic laws. However, the third law of information theory is different: for a solid structure of perfect symmetry (e.g., a perfect crystal), the entropy (static entropy for solid state) S is the maximum. More generally, a similarity principle is set up: if all the other conditions remain constant, the higher the similarity among the components is, the higher the value of entropy of the mixture (for fluid phases) or the assemblage (for a static structure or a system of condensed phases) or any other structure (such as quantum states in quantum mechanics) will be, the more stable the mixture or the assemblage will be, and the more spontaneous the process leading to such a mixture or an assemblage or a chemical bond will be.