  The delta-N formalism is considered to calculate the evolution of the
curvature perturbation in generalized multi-field inflation models. The result
is consistent with the usual calculation of the standard kinetic term. For the
calculation of the generalized kinetic term, we improved the definition of the
adiabatic field. Our calculation improves the usual calculation of the
evolution of the curvature perturbations based on the field equations and the
perturbations, giving a very simple and intuitive argument for the evolution
equations in terms of the perturbations of the inflaton velocity. Significance
of non-equilibrium corrections are also discussed, which is caused by the
small-scale (decaying) inhomogeneities. This formalism based on the modulated
inflation scenario (i.e., calculation based on the perturbations related to the
inflaton velocity) provides a powerful tool for investigating the signature of
moduli that may appear in string theory.
