Darwin-Fowler method

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A method for the derivation of the canonical and macro-canonical distributions from the micro-canonical distribution (cf. Gibbs distribution). One considers an ensemble of similar statistical systems which form a closed system on the whole, and its characteristic distribution function is summed over the microscopic states of all the systems in the ensemble except for one. It is assumed that the number of systems in the ensemble tends to infinity (if the number of particles in each one of the systems in the ensemble is large but finite); this makes it possible to use the saddle point method in computations. The use of this procedure to determine several common characteristics of statistical systems and to compute their concrete characteristics yields the same results as the method based on the Gibbs canonical distributions. The method was developed by Ch. Darwin and R. Fowler in 1923.


[1] R. Fowler, E. Guggenheim, "Statistical thermodynamics" , Cambridge Univ. Press (1960)
[2] K. Huang, "Statistical mechanics" , Wiley (1963)
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Darwin-Fowler method. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by I.A. Kvasnikov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article