Gas–Amorphous Solid and Liquid–Amorphous Solid Phase Transitions. Introduction of Negative Mass and Pressure from the Mathematical Viewpoint

We construct gas and liquid binodals assuming that both the gas and the liquid branch of the spinodal are given. To determine how the number of degrees of freedom depends on temperature, we use the main formula expressing the compressibility factor via the ratio of two Riemann functions. The behavior of the second virial coefficient is studied for a given spinodal, which serves as an analog of caustics. The gas– and liquid–amorphous solid transitions are considered on the second sheet. An argument in favor of the mapping of the second sheet onto the negative quadrant $\{-P,-Z\}$ is presented.