The line of maxima of fluctuations and the thermodynamic consistency of equations of state

In the work the behavior of fluctuations in the number of particles in the supercritical region was studied. In this case, to obtain the equations of state, the requirement of the highest possible thermodynamic consistency is used. This allows us to describe the shape of the ridge of fluctuations with an accuracy corresponding to the accuracy of the experimental data. In this case, we can establish the line of maxima of fluctuations, consistent with the experiment. This line makes it possible to find with a high degree of accuracy the density of the system at the critical point. Density is the last parameter of the critical point, when determining which, unlike temperature and pressure, difficulties arise. The proposed approach provides a way to solve this problem.