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Supercritical and critical states of fluids: new distribution and main invariants
For UD-statistics, we present formulas that are in agreement with the value of the second virial coefficient as $\rho\to 0$
at the initial point of the activity a\to 0 and with the temperature on the critical isochore rho=\rho_c at the final point.
This leads to two invariants: (1) the number of collective degrees of freedom and 2) the admissible size of the cluster fluctuation corresponding to a given temperature. In contrast to subcritical thermodynamics, in which the number of collective degrees of freedom undergoes a jump in the phase transition `` gas--liquid,'' the given invariants in supercritical hermodynamics remain valid on the whole isotherm. For rho>rho_c, using the van der Waals model, we see that fluids disintegrate into a cluster sponge and monomers. We show how these results can be carried over to real gases.