# Statistical mechanics of colloids and Boltzmann’s definition of the entropy

@article{Swendsen2006StatisticalMO, title={Statistical mechanics of colloids and Boltzmann’s definition of the entropy}, author={Robert H. Swendsen}, journal={American Journal of Physics}, year={2006}, volume={74}, pages={187-190} }

The Boltzmann entropy as traditionally presented in statistical mechanics textbooks is only a special case and not Boltzmann's fundamental definition. The difference becomes important when the traditional expression for the entropy is applied to colloids, for which it makes incorrect predictions. Boltzmann's original definition of the entropy in terms of the probabilities of states of composite systems leads to consistent and correct statistical mechanics and thermodynamics.

## 53 Citations

Thermodynamics of the System of Distinguishable Particles

- Physics, Computer Science
- 2009

The issue of the thermodynamics of a system of distinguishable particles is discussed and a straightforward way to get the corrected Boltzmann counting is shown, which can be justified in classical statistical mechanics.

Thermodynamics of the System of Distinguishable Particles

- Physics, Computer ScienceEntropy
- 2009

The issue of the thermodynamics of a system of distinguishable particles is discussed and a straightforward way to get the corrected Boltzmann counting is shown, which can be justified in classical statistical mechanics.

Continuity of the entropy of macroscopic quantum systems.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

This paper analyzes and calculates the thermodynamic entropy for large but finite quantum mechanical systems and preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics.

Gibbs volume entropy is incorrect.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

We show that the expression for the equilibrium thermodynamic entropy contains an integral over a surface in phase space, and in so doing, we confirm that negative temperature is a valid…

Gibbs' Paradox and the Definition of Entropy

- Physics, Computer ScienceEntropy
- 2008

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.

Choosing a Definition of Entropy that Works

- Computer Science
- 2012

The consequences of differing definitions of the thermodynamic entropy of macroscopic systems are examined and a definition based on probabilities is argued in favor.

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

- Physics
- 2014

Colloidal particles are distinguishable. Moreover, their thermodynamic properties are extensive. Statistical mechanics predicts such behaviour if one accepts that the configurational integral of a…

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