The lines of extremes for the second derivatives of the Gibbs potential in the supercritical regions of substances

A parametric expression for the Gibbs potential was found using the generalized Van Laar method for the free energy of a system. Since this expression is used in order to analyze the behavior of a system in the supercritical region, the well-studied system of soft spheres was selected as a reference system. This allows one to find thermodynamic characteristics from known virial coefficients of the system and available information on the position of the critical point. The lines of the extremes for the second derivatives of the Gibbs potential were calculated for a system with the Lennard-Jones interaction potential. The line of the maxima of the isothermal compressibility and the line of the maxima of the constant-pressure heat capacity were compared with the molecular-dynamics data. The good agreement between the theoretical calculations, which are based on analytic functions in this domain, and the molecular-dynamics data shows the absence of a third-order phase transition in the supercritical region.