This page was last edited on 05/04/02 by Malcolm R Forster

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Khinchin.pdf (53 double-spaced pages, 649 KB.)

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1. Introduction

2. Time Invariance and Liouville’s theorem

3. Time-Invariant Probabilities on an Energy Surface

4. Probabilities and the Structure Function

5. Extended Ensembles and the Central Limit Theorem

6. The Method of Approximation

7. The Kullback-Leibler Payoffs

8. The Large Component Approximation

9. A Geometrical Interpretation of Khinchin’s Construction

10. The Small Component Approximation

11. The Meaning of Temperature in ‘Nice’ Examples

12. Particles in a Uniform Field of Force

13. General Conclusion

14. Appendix

This is obviously going to become a book.

 This paper began life as a serious attempt to understand the foundations of classical thermodynamics, but ended up doing crazy things like defining the temperature and entropy of single molecules.  Nevertheless, there is method behind the madness, because in terms of these generalized definitions I am able to prove that the generalized notion of temperature reduces to the standard notion under certain quite general conditions, in which case the standard entropy is equal to the sum of the molecular entropies. The generalized viewpoint is intended to provide a deeper understanding of how statistical mechanics works, …and why it doesn’t work, sometimes, as in the case of a single particle in a box.  The purpose of such examples is to make a conceptual point, not to advance physics.