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A modernized version of Gibbs' use of the grand canonical ensemble

Published online by Cambridge University Press:  24 October 2008

R. H. Fowler
R. H. Fowler
Affiliation:
Trinity College
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Extract

In the last chapter of his Introduction to statistical mechanics Gibbs introduces the idea of the grand canonical ensemble. He had previously determined the properties of an assembly or a phase containing a given number of systems by averaging the properties of the assembly over an ensemble of examples canonically distributed in phase, keeping the number of systems in the assembly fixed. This means of course constructing what we now call the partition function for the assembly by summing or integrating e−E/kT over the whole of the accessible phase space.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 3 , July 1938 , pp. 382 - 391
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

* Milner, , Phil. Mag. 23 (1912), 551CrossRefGoogle Scholar and 25 (1913), 743.

† Kramers, , Proc. Acad. Sci. Amsterdam, 30 (1927), 145.Google Scholar

‡ Bethe, , Proc. Roy. Soc. A, 150 (1935), 552.CrossRefGoogle Scholar See also Easthope, , Proc. Cambridge Phil. Soc. 33 (1937), 502.CrossRefGoogle Scholar

§ Peierls, , Proc. Roy. Soc. A, 154 (1936), 207.CrossRefGoogle Scholar

* Fowler, , Statistical mechanics, 2nd ed. (Cambridge, 1936).Google Scholar Equation (583) yields (6) on slight rearrangement. Further references to this book will be given as S.M.

† S.M. equation (603).

† S.M. equation (138).

* Cf. S.M. equation (220).

* S.M. §§ 21·53 sqq.

* S.M. § 21·58.

† Peierls, , Proc. Cambridge Phil. Soc. 32 (1936), 471.CrossRefGoogle Scholar