  We introduce a novel freeze-out procedure connecting the hydrodynamic
evolution of a droplet of quark-gluon plasma (QGP) that has, as it expanded and
cooled, passed close to a posited critical point on the QCD phase diagram with
the subsequent kinetic description in terms of observable hadrons. The
procedure converts out-of-equilibrium critical fluctuations described by
extended hydrodynamics, known as Hydro+, into cumulants of hadron
multiplicities that can be subsequently measured. We introduce a critical sigma
field whose fluctuations cause correlations between observed hadrons due to the
couplings of the sigma field to the hadrons. We match the QGP fluctuations
obtained via solving the Hydro+ equations describing the evolution of critical
fluctuations before freeze-out to the correlations of the sigma field. In turn,
these are imprinted onto fluctuations in the multiplicities of hadrons, most
importantly protons, after freeze-out via a generalization of the familiar
half-a-century-old Cooper-Frye freeze-out prescription which we introduce. This
framework allows us to study the effects of critical slowing down and the
consequent deviation of the observable predictions from equilibrium
expectations quantitatively. We can also quantify the suppression of cumulants
due to the conservation of baryon number. We demonstrate the prescription in
practice by freezing out the Hydro+ simulation in a simplified azimuthally
symmetric and boost invariant background discussed in Rajagopal, Ridgway,
Weller, Yin, 2019.
