Why colloidal systems can be described by statistical mechanics: some not very original comments on the Gibbs paradox

2013/12/31 by Daan Frenkel · 1 voice · 2 citations
Chemical Engineering · Engineering · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Phase Equilibria and Thermodynamics #Thermodynamic properties of mixtures

paper · pdf · doi:10.1080/00268976.2014.904051

openalex publication_date 2014/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Colloidal particles are distinguishable. Moreover, their thermodynamic properties are extensive. Statistical mechanics predicts such behaviour if one accepts that the configurational integral of a system of N colloids must be divided by N!. In many textbooks, it is argued that the factor N! corrects for the fact that identical particles (in the quantum mechanical sense) are indistinguishable. Clearly, this argument does not apply to colloids. This article explains why, nevertheless, all is well. The point has been made before, but has not yet sunk in. I also discuss the effect of polydispersity.

Citations

• Ueber das Gesetz der Energieverteilung im Normalspectrum

Cited by

• Active sorting of particles as an illustration of the Gibbs mixing\n paradox
• Energy and information: a chronicle of hesitations on the role of the observer in physics

Discussions

• I believe your question can be summarised as: if two systems of particles interact via identical forces and evolve under the same dynamics, how can they exhibit different equilibrium distributions mer [stackexchange, 4 points]

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