  In recent publications we proposed one way to calculate gauge-invariant
variables in the local observable universe, which is limited to a portion of
the whole universe. To provide a theoretical prediction of the observable
fluctuations, we need to preserve the gauge-invariance in the local universe,
which is referred to the genuine gauge-invariance. The importance of the
genuine gauge-invariance is highlighted in the study of primordial fluctuations
in the infrared (IR) limit. The stability against IR loop corrections to
primordial fluctuations is guaranteed in requesting the genuine
gauge-invariance. The genuine gauge-invariance also gives the impact on the
detectable fluctuations. We showed that at observable scales the bi-spectrum
calculated in the conventional perturbation theory vanishes in the squeezed
limit, if we request the genuine gauge invariance. This indicates that the
conventional bi-spectrum is, in this limit, dominated by a gauge artifact,
which cannot be observed. These studies have been elaborated in single-field
models of inflation. In this paper we generalize our argument to multi-field
models of inflation, where, in addition to the adiabatic field, the entropy
field can participate in the generation of primordial fluctuations. We will
find that the entropy field can generate the observable fluctuations, which
cannot be eliminated by gauge transformations in the local universe.
