  This paper first establishes an approximate scaling property of the
potential-energy function of a classical liquid with good isomorphs (a
Roskilde-simple liquid). This "pseudohomogeneous" property makes explicit that
- and in which sense - such a system has a hidden scale invariance. The second
part gives a potential-energy formulation of the quasiuniversality of monatomic
Roskilde-simple liquids, which was recently rationalized in terms of the
existence of a quasiuniversal single-parameter family of reduced-coordinate
constant-potential-energy hypersurfaces [J. C. Dyre, Phys. Rev. E 87, 022106
(2013)]. The new formulation involves a quasiuniversal reduced-coordinate
potential-energy function. A few consequences of this are discussed.
