  We attempt to relate two recent developments: cluster algebras associated to
triangulations of surfaces by Fomin-Shapiro-Thurston, and quivers with
potentials and their mutations introduced by Derksen-Weyman-Zelevinsky. To each
ideal triangulation of a bordered surface with marked points we associate a
quiver with potential, in such a way that whenever two ideal triangulations are
related by a flip of an arc, the respective quivers with potentials are related
by a mutation with respect to the flipped arc. We prove that if the surface has
non-empty boundary, then the quivers with potentials associated to its
triangulations are rigid and hence non-degenerate.
