Investigating the partonic entanglement entropy at low Bjorken-x within Gluon saturation approach

In this work, the entanglement entropy is examined within the context of deep inelastic scattering in $ep$ collisions. The calculation is based on a formalism where the partonic state at small- $x$ is maximally entangled, consisting of a large number of micro-states occurring with equal probabilities. Analytical expressions for the number of gluons, $N_{\text{gluon}}$, are considered, derived from gluon saturation models for dipole-target amplitudes within the framework of the Quantum Chromodynamics (QCD) color dipole picture. A comparison of the entanglement entropy with thermodynamic entropy measured in $pp$ and $ep$ collisions at high energies is done.