Looking at the Entropy in a Proton through a QGP Lens

TL;DR

This paper explores how quantum entanglement entropy within hadrons accounts for the thermodynamic entropy of quark-gluon plasma during the quark-hadron phase transition, linking microscopic quantum states to macroscopic thermodynamics.

Contribution

It provides three different estimates of the proton's internal entanglement entropy and demonstrates its similarity to the QGP entropy, offering a new perspective on confinement and phase transition.

Findings

Entanglement entropy of the proton is comparable to the Gibbs entropy of QGP.

Reorganization of entropy during hadronization involves quantum correlations.

Different estimation methods yield consistent entropy magnitudes.

Abstract

We investigate the interplay between the thermodynamic (Gibbs) entropy of quark-gluon plasma (QGP) and the quantum entanglement entropy characteristic of confined hadronic states across the quark-hadron phase transition. In the deconfined regime, entropy is well described by the statistical mechanics of colored quarks and gluons. Upon hadronization, however, the macroscopic Gibbs entropy of the plasma cannot simply vanish; instead, it is reorganized into the configurational entropy of a gas of colorless hadrons together with quantum correlations among the confined partons within each hadron. We show that the entanglement entropy of the internal partonic wave functions inside hadrons provides a natural repository for this ``converted'' thermodynamic entropy, reconciling the apparent reduction of macroscopic entropy with the second law of thermodynamics. Either by extrapolating from known facts about deep inelastic scattering, or starting from model descriptions of the proton wave function, or starting from the Hagedorn spectrum of its resonances, we provide three estimates of the magnitude of the entanglement entropy carried by a proton, with very different uncertainties. All three estimates indicate that the internal entanglement entropy of the proton is similar in magnitude to the Gibbs entropy of the QGP droplet from which the proton formed as QGP cools through the quark-hadron transition, as for example throughout the universe microseconds after the Big Bang. These results suggest that entanglement entropy offers a bridge between the quantum information content of hadronic states and the thermodynamic entropy of the quark-gluon plasma, providing a new lens on the microscopic mechanism of confinement and the nature of the QCD phase transition.