Exploring Particle Production and Thermal-like Behavior in Relativistic Particle Collisions Through Quantum Entanglement

Thermal-like features in hadron production are observed in small systems such as proton–proton interactions, where conventional kinetic equilibration on sub-fm/c time scales is challenging to justify. One proposed explanation is that quantum entanglement in the incoming hadron wave functions, together with coarse-graining over unobserved degrees of freedom, can generate an entropy-like signal without requiring extensive final-state rescattering. We test whether a final-state Shannon entropy extracted from the charged-particle multiplicity distributions measured by ALICE at s=0.9–8 TeV can be reproduced by an initial-state entanglement entropy computed from leading-order proton PDFs. In a low-x approximation where the reduced density matrix of the probed region is taken to be maximally mixed in an effective parton-number basis, the entanglement entropy reduces to SEE≃lnN, where N is obtained by integrating PDFs over an x-range mapped from the ALICE midrapidity acceptance. We include gluon and sea-quark contributions and apply correction factors accounting for the charged fraction and the limited set of measured degrees of freedom. Within the stated assumptions and PDF uncertainties, the initial- and final-state entropy become numerically compatible toward low x, supporting the interpretation that initial-state quantum entanglement can contribute to the apparent thermal-like behavior in small collision systems.