In some theories, the energy is predicted to have this funny shape. The concave region is not allowed, so the simplest idea is just to fill the region with a segment (to form a “convex hull”). This is called the common tangent construction, and it is related to very classic Maxwell construction. Originally, JC Maxwell used this construction when analyzing results from the van der Waals equation of state for fluids.

The wikipedia article on Maxwell construction is fine, but the related common tangent construction does not exist! (you can create it if you feel like it). I have therefore written down these notes with information about this construction. Very simple, really, but my thermodynamics was very rusty!