  Based on rare fluctuations in strong interactions, we argue that there is a
strong physical resemblance between the high multiplicity events in
photo-nuclear collisions and those in $pA$ collisions, in which interesting
long range collective phenomena are discovered. This indicates that the
collectivity can also be studied in certain kinematic region of the upcoming
Electron-Ion Collider (EIC) where the incoming virtual photon has a
sufficiently long lifetime. Using a model in the Color Glass Condensate
formalism, we first show that the initial state interactions can explain the
recent ATLAS azimuthal correlation results measured in the photo-nuclear
collisions, and then we provide quantitative predictions for the long range
correlations in $eA$ collisions in the EIC regime. With the unprecedented
precision and the ability to change the size of the collisional system, the
high luminosity EIC will open a new window to explore the physical mechanism
responsible for the collective phenomenon.
