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The number-theoretical problem of partition of an integer corresponds to$D=2$. This problem obeys the Bose--Eeinstein statistics, where repeated termsare admissible in the partition, and to the Fermi--Dirac statistics, where theyare inadmissible. The Hougen--Watson P,Z-diagram shows that this problem splitsinto two cases: the positive pressure domain corresponds to the Fermi system,and the negative, to the Bose system. This analogy can be applied to the vander Waals thermodynamics.  The thermodynamic approach is related to four potentials corresponding to theenergy, free energy, thermodynamic Gibbs potential, enthalpy. The importantnotion of de Broglie's wavelength permits passing from particle to wave packet,in particular, to Bose and Fermi distributions.  Particles of ideal Bose and Fermi gases and the decay of a boson consistingof two fermions into separate fermions are studied. The case of finitely manyparticles $N$ of the order of $10^2$ is considered by heuristic considerationslike those Fock used to derive the Hartree--Fock equation. The case of $N\ll1$is studied by Gentile statistics, tropical geometry and nonstandard analysis(Leibnitz differential or monad). A relation for the energy of neutronseparation from the atomic nucleus is obtained when the atomic nucleus volumeand de Broglie's wavelength are known. The Appendix is author's paper writtenin 1995.

Bose Condensate in the D-Dimensional Case, in Particular, for D=2. Semiclassical transition to the classical thermodynamics