Darwin–Fowler method
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Darwin-Fowler method
In most texts on statistical mechanics the statistical distribution functions (Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac) are derived by determining those for which the system is in its state of maximum probability. But one really requires those with average or mean probability, although - of course - the results are usually the same for systems with a huge number of elements, as is the case in statistical mechanics. The method for deriving the distribution functions with mean probability has been developed by C.G. Darwin and R.H. Fowler and is therefore known as the Darwin-Fowler method. This method is the most reliable general procedure for deriving statistical distribution functions. Since the method employs a selector variable (a factor introduced for each element to permit a counting procedure) the method is also known as the Darwin-Fowler method of selector variables.
The Darwin-Fowler method has been treated in the texts of Schrödinger[1], Fowler[2] and Fowler and Guggenheim [3], by Huang[4], and Müller-Kirsten[5]. The method is also discussed and used for the derivation of Bose-Einstein condensation in the book of Dingle[6].
References
- ^ E. Schrödinger, Statistical Thermodynamics, Cambridge University Press (1952).
- ^ R.H. Fowler, Statistical Mechanics, Cambridge University Press (1952).
- ^ R.H. Fowler and E. Guggenheim, Statistical Thermodynamics, Cambridge University Press (1960).
- ^ K. Huang, Statistical Mechanics, Wiley (1963).
- ^ H.J.W. Müller-Kirsten, Introduction to Statistical Physics, 2nd ed., World Scientific (2013).
- ^ R.B. Dingle, Asymptotic Expansions: Their Derivation and Interpretation, Academic Press (1973); pp. 267-271.