Main axiom of thermodynamics and entropy of number theory: Tunnel and ultrasecond quantization

We single out the main features of the mathematical theory of equilibrium thermodynamics. The theory of Bose condensate is expressed as a problem in number theory and its relation to various evolutionary processes is studied. It is proved that the points of degeneracy of the Bose gas fractal dimension in momentum space coincide with the critical points of imperfect gases, while the jumps of the critical indices and the Maxwell rule are related to tunnel quantization in thermodynamics. We consider semiclassical methods for tunnel quantization in thermodynamics as well as those for second and third quantization.