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

  title={Why colloidal systems can be described by statistical mechanics: some not very original comments on the Gibbs paradox},
  author={Daan Frenkel},
  journal={Molecular Physics},
  pages={2325 - 2329}
  • D. Frenkel
  • Published 1 December 2013
  • Physics
  • Molecular Physics
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… 
Probability, Entropy, and Gibbs’ Paradox(es)
It is shown that contrary to what has often been suggested, quantum mechanics is not essential for resolving the paradoxes and includes the case of colloidal solutions, for which quantum Mechanics is not relevant.
Celebrating Soft Matter's 10th anniversary: Testing the foundations of classical entropy: colloid experiments.
The experimental facts point firmly to an 'informatic' interpretation that dates back to Gibbs: entropy is determined by the number of microstates that the authors as observers choose to treat as equivalent when they identify a macrostate.
Does the configurational entropy of polydisperse particles exist?
It is shown how to directly determine M* from computer simulations in a range of glass-forming models with different size polydispersities, characterized by hard and soft interparticle interactions, and by additive and non-additive interactions.
On the role of composition entropies in the statistical mechanics of polydisperse systems
This paper addresses the issue of defining a non-ambiguous combinatorial entropy for polydisperse systems by focusing on the general property of extensivity of the thermodynamic potentials and discussing a specific mixing experiment, and introduces the new concept of composition entropy for single phase systems that do not assimilate to a mixing entropy.
The Gibbs paradox
Molecular collision within an ideal gas originates from an intrinsic short-range repulsive interaction. The collision reduces the average accessible physical space for a single molecule and this has
Numerical test of the Edwards conjecture shows that all packings are equally probable at jamming
Numerical simulation now demonstrates that all distinct packings are equally probable in granular media — precisely at the jamming threshold — and presents evidence that at unjamming the configurational entropy of the system is maximal.
On the Logic of a Prior Based Statistical Mechanics of Polydisperse Systems: The Case of Binary Mixtures
It is found that (a) there exist circumstances for which an ideal binary mixture is thermodynamically equivalent to a single component ideal gas and (b) even when mixing two substances identical in their underlying composition, entropy increase does occur for finite size systems.
Gibbs’ paradox according to Gibbs and slightly beyond
The statistical thermodynamics of discrete and continuous mixtures is turned to and the notion of composition entropy is introduced to characterise these systems to address a ‘curiosity’ pointed out by Gibbs in a paper published in 1876.
Edwards Statistical Mechanics for Jammed Granular Matter
In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical
Polydisperse Colloids Two-Moment Diffusion Model Through Irreversible Thermodynamics Considerations
Abstract This study deals with the problem of diffusion for polydisperse colloids. The resolution of this complex problem usually requires computationally expensive numerical models. By considering


Statistical mechanics of colloids and Boltzmann’s definition of the entropy
The Boltzmann entropy as traditionally presented in statistical mechanics textbooks is only a special case and not BoltZmann's fundamental definition, which leads to consistent and correct statistical mechanics and thermodynamics.
The Gibbs Paradox
We point out that an early work of J. Willard Gibbs (1875) contains a correct analysis of the “Gibbs Paradox” about entropy of mixing, free of any elements of mystery and directly connected to
Gibbs' Paradox and the Definition of Entropy
Gibbs’ Paradox is shown to arise from an incorrect traditional definition of the entropy that has unfortunately become entrenched in physics textbooks, which predicts a violation of the second law of thermodynamics when applied to colloids.
Information Theory and Statistical Mechanics
Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between
Tracing the phase boundaries of hard spherocylinders
We have mapped out the complete phase diagram of hard spherocylinders as a function of the shape anisotropy L/D. Special computational techniques were required to locate phase transitions in the
Maximum Entropy and Bayesian Methods.
Abstract : This volume contains selections from among the presentations at the Thirteenth International Workshop on Maximum Entropy and Bayesian Methods- MAXENT93 for short- held at the University of
Ueber das Gesetz der Energieverteilung im Normalspectrum
Die neueren Spekfralmessungen von O. Lummer und E. Pringsheim 4) und noch auffalliger diejenigen von H. Rubens und F. Kurlbaum 5), welche zugleich ein frUher von H. Beckmann 1) erhaltenes Resultat
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
  • Rev. Lett. 80, 1369
  • 1998