Characterizing the initial state of hydrodynamics in pp and pA collisions

The observation of seeming hydrodynamic-like behavior in proton-proton and proton-nucleus collisions presents us with the conceptual problem of how the initial state of such a hydrodynamic evolution should be characterized. This is an issue because, while nuclei can reasonably be approximated as ``large'' systems w.r.t. the characteristic Fermi momentum of their constituents, this is no longer true for nucleons. Hence, one would need to match a ``quantum'' theory, whose observables are described via highly non-commuting operators, to a ``classical'' hydrodynamics. Operationally assuming a ``fast'' thermalization, we survey what kind of object is best suited to such a matching condition. We show that it cannot be any of the objects usually associated with ``the 3D structure of the nucleon'' but rather a measure associated with entanglement entropy.