Hydrodynamical Initial State in Small Systems From the Phase-Space Entropy

Abstract

The experimental observation of collective behavior in proton-proton and proton-nucleus collisions poses a fundamental theoretical question regarding the proper characterization of the initial state underlying hydrodynamic evolution. While relativistic hydrodynamics requires an initial condition characterized by an entropy current, corresponding to a maximally mixed state, the microscopic description of the proton is based on inherently quantum objects that probes projections of pure states. We show that the appropriate matching between hadronic structure and classical hydrodynamics emerges from the coarse-graining of the partonic Wigner distribution, leading naturally to a Husimi distribution and its associated Wehrl entropy. This entropy provides a semiclassical, positive-definite measure of the density of accessible microstates at a given resolution scale, and therefore constitutes the appropriate quantity to characterize entropy deposition in small collision systems.

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