Page entropy of a proton system in deep inelastic scattering at small x

The partons model reveals the dynamical structure of nucleons (protons and neutrons). Studies related to thermodynamic quantities of nucleons present interesting and topical questions. In this work, for the first time we apply Page's theory of the studies of black holes to investigate the entropy of a proton system. Inspired by the quantum entanglement entropy in black hole information theories, we establish the proton entanglement with the similar way. Based our calculations, the proton entanglement entropy has the approximate form S=lnm-1/2, where m represents the partons density of proton (mainly gluon and sea quark contributions) at small Bjorken x. Our calculations using Page's theory are well in agreement with the recent deep inelastic scattering measurements from the H1 Collaboration.