This surface shows another first Legendre transform, but the function has no common name. It is referred to (extensively) as U´. The mathematical definition is U´ = U - µN = TS – PV. Volume is the scaling factor in this data set so that the function actually plotted is

The tangent line represents a fixed chemical potential (µ = G for the pure material), and the surface has been differenced for vertical magnification. Variables scaled by volume are often referred to as "densities," thus SV = entropy density, Udv = differenced energy density.

Iowa State University