At the Large Hadron Collider, not only nuclei but also individual protons collide. Even in such small systems, collective behavior resembling the flow of a liquid is observed. But the proton is a quantum object; its state is described by a wave function, not by temperature and pressure. How does the classical picture emerge from the quantum 'mosaic'?

Hydrodynamics requires initial conditions set by the entropy flux — a measure of disorder. The quantum state of a proton is a projection of a pure state, whose entropy is zero.

The authors propose using the Weyl entropy, which arises from coarse-graining phase space — averaging over small cells. Such entropy is always positive and provides a semiclassical measure of the number of accessible microstates at a given resolution. It is precisely this entropy that allows linking the quantum wave function of the proton to the classical initial conditions for hydrodynamics.

This is akin to translating a mosaic into a painting: if you look at the mosaic too closely, you see individual pieces (quantum states), but step back, and they merge into a unified canvas (hydrodynamic description). The Weyl entropy is the tool that measures the degree of this merging.