# 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.

## 54 Citations

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## References

SHOWING 1-3 OF 3 REFERENCES

### Fundamentals of Statistical and Thermal Physics

- Education
- 1965

This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical…

### Statistical Mechanics of Classical Systems with Distinguishable Particles

- Computer Science
- 2002

The properties of classical models of distinguishable particles are shown to be identical to those of a corresponding system of indistinguishable particles without the need for ad hoc corrections. An…