Low temperature properties of the Fermi-Dirac, Boltzmann and Bose-Einstein equations

We investigate low temperature (T) properties of three classical quantum statistics models: (I) the Fermi-Dirac equation, (II) the Boltzmann equation, and (III) the Bose-Einstein equation. It is widely assumed that each of these equations is valid for all T > 0. For each equation we prove that this assumption leads to erroneous predictions as T -> 0(+). Our approach to correct these errors gives new low temperature predictions which contradict previous theory. We examine a two-state paramagnetism system and show how our new low temperature prediction compares favorably with experimental data. (C) 2012 Elsevier B.V. All rights reserved.