For the collective gravithermodynamic Gibbs microstates the connection between all thermodynamic potentials and parameters of matter have been found. This connection is realized with the help of four hidden wave functions that can take arbitrary values with certain probability. The possibility of obtaining the known equations of thermodynamic state of real gases is shown based on the use of both their the limit velocities of individual (separate) motion and the mathematicalexpectations precisely of these four nonspecific hidden parameters (wave functions) and functions of them. It is substantiated that in a quasi-equilibrium state, a real gas has spatial homogeneity not only of its entropy but also of the resulting extensive parameter (an indicator the compressibility coefficient). But the radial values of resulting intensive parameter (an indicator of hierarchical complexity and of quasi-equilibrium of cooling down) of a real gas are invariant in time.