On the kinetic method in the new statistics and application in the electron theory of conductivity

Abstract

Hitherto in work on the new statistics the method of probabilities has always been used, a method which consists in the measuring of the phase space by counting complexions. Now this method is certainly very useful and valuable on account of its generality and convenience, but it has the drawback that only equilibrium states and fluctuations can be treated, not the more general streaming and conductivity phenomena. In the classical physics a method for such problems has been created in the dynamical theory of gases by Max­ well and Boltzmann, and it seems therefore useful to try to adapt it to the new statistics. That task has become particularly necessary, because a corresponding method, due to H. A. Lorentz, has been applied by Sommerfeld* in his theory of metallic conductivity. As it will be shown, the dynamical theory can be worked out in the new statistics, both for the Einstein-Bose and the Fermi-Dirac statistics, in a way completely analogous to the corresponding one of Boltzmann, only some characteristic additional terms occurring. The latter, however, just cancel out in the special case of the electronic conductivity under certain assumptions, so that Sommerfeld’s procedure is justified.