  We discuss the treatment, in an effective field theory, of multi-particle
correlations within a "large" system. We show that the act of coarse-graining
necessarily introduces violations of unitarity in the evolution of states where
the particle number is not defined. For an interacting system, such unitarity
violations can cascade from the ultraviolet scale to the infrared in a "short"
time. Hence, an effective field theory will be grossly inadequate for
describing multi-particle correlations and related observables, even far away
from the cut-off scale $\Lambda$. We furthermore argue that if the system is
strongly coupled at $\Lambda$, than its final state {\em in the Effective Field
Theory} (EFT) will appear as the highest entropy state if only low cumulants
and correlations of the EFT degrees of freedom are measured.
  Heuristically, this can serve as an explanation of how "entropy" is created
in a microscopically unitary evolution of a Quantum Field Theory (QFT). We
conclude by discussing how these considerations might provide a clue to the
apparent thermalization in a hadronic collision even in comparatively small
systems, as well as the so-called black hole information paradox; We argue the
"paradoxes" are likely to be artifacts of using an effective theory beyond its
domain of validity.
