Flavor--Kinetic Entanglement Production from Decay and Scattering at Finite Density

Abstract

We extend the scattering-entanglement dictionary to finite-density environments by investigating the flavor--kinetic bipartition of the Hilbert space. We show that tracing over kinematic degrees of freedom maps the total branch-changing transition probability directly onto the leading flavor--kinetic linear entanglement entropy. At finite density, the vacuum branch-changing probability is replaced by an occupation-weighted collision probability, built from the same directed reaction-density kernel that enters the integrated Boltzmann equation. The resulting observable is the bath-averaged flavor--kinetic entanglement entropy of a pair sampled from the medium. As a proof of principle, this framework is applied to an $O(N)$ singlet-scalar extended model to probe thermal phase transitions. In the examples studied, the resulting entanglement entropy serves as a collision-based phase-transition-type diagnostic, exhibiting a finite discontinuity across a first-order phase transition and a nonanalytic temperature derivative for continuous transitions. These examples suggest a novel way to characterize thermal phase structures, distinct from traditional thermodynamic order parameters.