  Potential functionals have been introduced recently as an important tool for
the analysis of coupled scalar systems (e.g. density evolution equations). In
this contribution, we investigate interesting properties of this potential.
Using the tool of displacement convexity, we show that, under mild assumptions
on the system, the potential functional is displacement convex. Furthermore, we
give the conditions on the system such that the potential is strictly
displacement convex, in which case the minimizer is unique.
