Summary The origin of Gibbs' canonical ensemble and the associated partition sum is briefly discussed. It is then shown that for assemblies of particles obeying the Boltzmann, Einstein-Bose or Fermi-Dirac conditions the partition sum possesses some simple properties from which the known expressions for the average distribution in energy of particles are derived elementarily without reference to either Stirling's formula or the method of steepest descent.
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Ansbacher et al. (1949) studied this question.
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