  In the paper, the principal aspects of the mathematical theory of equilibrium
thermodynamics are distinguished. It is proved that the points of degeneration
of a Bose gas of fractal dimension in the momentum space coincide with critical
points or real gases, whereas the jumps of critical indices and the Maxwell
rule are related to the tunnel generalization of thermodynamics. Semiclassical
methods are considered for the tunnel generalization of thermodynamics and also
for the second and ultrasecond quantization (operators of creation and
annihilation of pairs). To every pure gas there corresponds a new critical
point of the limit negative pressure below which the liquid passes to a
dispersed state (a foam). Relations for critical points of a homogeneous
mixture of pure gases are given in dependence on the concentration of gases.
