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.