Thermodynamics of van der Waals fluids with quantum statistics

We consider thermodynamics of the van der Waals fluid of quantum systems. We derive general relations of thermodynamic functions and parameters of any ideal gas and the corresponding van der Waals fluid. This provides unambiguous generalization of the classical van der Waals theory to quantum statistical systems. As an example, we apply the van der Waals fluid with Fermi statistics to characterize the liquid-gas critical point in nuclear matter. We also introduce the Bose–Einstein condensation in the relativistic van der Waals boson gas, and argue that it exhibits two-phase structure separated in space