The temperature-entropy-pressure relation as derived from the HSP fundamental equation. As shown by other analogous functions, thermodynamic stability depends on the sign of the local curvature of the parent fundamental form. For stable states on the HSP surface

In this drawing all states in the blue and yellow regions slope upward and satisfy this criterion. Viewed from the front (i.e., in the pressure direction) and with the red and yellow regions replaced by horizontal tie lines, this function yields the conventional T-S diagram.

Iowa State University