  The dynamics of bosons in generic multimode systems, such as Bose-Hubbard
models, is not only determined by interactions among the particles, but also by
their mutual indistinguishability manifested in many-particle interference. We
introduce a measure of indistinguishability for Fock states of bosons whose
mutual distinguishability is controlled by an internal degree of freedom. We
demonstrate how this measure emerges both in the non-interacting and
interacting evolution of observables. In particular, we find an unambiguous
relationship between our measure and the variance of single-particle
observables in the non-interacting limit. A non-vanishing interaction leads to
a hierarchy of interaction-induced interference processes, such that even the
expectation value of single-particle observables is influenced by the degree of
indistinguishability.
