  We give an explicit relation, up to second-order terms, between scalar-field
fluctuations defined on spatially-flat slices and the curvature perturbation on
uniform-density slices. This expression is a necessary ingredient for
calculating observable quantities at second-order and beyond in multiple-field
inflation. We show that traditional cosmological perturbation theory and the
`separate universe' approach yield equivalent expressions for superhorizon
wavenumbers, and in particular that all nonlocal terms can be eliminated from
the perturbation-theory expressions.
