Two-fluid picture of supercritical phenomena

We consider a parastatistics that does not distinguish objectively different objects but describes clusters in the supercritical state and determines the relation between the mesoscopic physics of clusters and the macroscopic thermodynamics of supercritical isotherms. We construct the supercritical picture of isochores and isotherms under the condition that the Boyle temperature, the Boyle density, and the critical point are known, and we justify the two-fluid model of supercritical thermodynamics mathematically. For the "cluster sponge," this leads to new relations different from the relations of the known Gentile statistics. We calculate the Frenkel temperature of the transition from rigid liquid to soft liquid.