For the collective gravithermodynamic Gibbs microstates the connection betweenall thermodynamic potentials and parameters of matter have been found. Thisconnection is realized with the help of four hidden wave functions that can takearbitrary values with certain probability. The possibility of obtaining the knownequations of thermodynamic state of real gases is shown based on the use of boththe coordinate velocity of light of the general relativity and the mathematicalexpectations precisely of these four hidden parameters (wave functions) andfunctions of them. It is substantiated that in a quasi-equilibrium state, a real gashas spatial homogeneity not only of its entropy but also of the resulting extensiveparameter (an indicator the compressibility coefficient). But the radial values ofresulting intensive parameter (an indicator of hierarchical complexity and ofquasi-equilibrium of cooling down) of a real gas are invariant in time. It has beenproven that the orthodox interpretation of general relativity is not consistent withgradually cooling matter and therefore with the evolutionary cooling of the earlyUniverse.