Remarks on Number Theory and Thermodynamics Underlying Statistical Distributions in Languages

In the paper “The relationship between the Fermi–Dirac distribution and statistical distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac distributions are considered in connection with frequency distributions in languages in the context of the author's approach to thermodynamics and number theory problems. The present article presents certain clarifications of certain notions used in that approach, in particular, the identity of particles, the Poisson adiabat, the matching of number theory formulas with those given by the Bose–Einstein distribution, nonstandard analysis, and others.