Entropy from decoherence: a case study using glasma-based occupation numbers

We compute the entropy-per-particle, $S/N$, produced by the decoherence of a coherent state interacting with an environment, using an analytical open quantum system approach. The coherent state considered is characterized by occupation numbers borrowed from the glasma fields produced in the early stages of high-energy nuclear collisions. The environment is modeled as the vacuum, and decoherence arises from the interaction of the state with vacuum fluctuations. We describe the system-environment interaction via a phase-damping model, which represents continuous measurements on the system without altering its energy or particle number. Starting from the occupation numbers typical of the Glasma in high-energy proton-nucleus and nucleus-nucleus collisions, we find that the final $S/N$ after decoherence is lower than that of a two-dimensional thermal bath of ultrarelativistic gluons, except for proton-nucleus collisions at small values of $g\mu$. Our results indicate that quantum decoherence alone does not generate sufficient entropy to transform the initial coherent state into a thermalized gluon bath.