The fundamental difference between classical (isothermal) nucleation theory (CNT) and adiabatic nucleation theory (ANT) is discussed. CNT uses the concept of isothermal heterophase fluctuations, while ANT depends on common fluctuations of the thermodynamic variables. Applications to the nonequilibrium liquid to vapor transition are shown. However, we cannot yet calculate nucleation frequencies. At present, we can only indicate at what temperatures and pressures copious homogeneous nucleation is expected in the liquid to vapor phase transition. It is also explained why a similar general indication cannot be made for the inverse vapor to liquid transition. Simultaneously, the validity of Peng-Robinson's equation of state [D.-Y. Peng and D. B. Robinson, Ind. Eng. Chem. Fundam. 15, 59 (1976)] is confirmed for highly supersaturated liquids.