Page entropy of a proton system in deep inelastic scattering at small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math>

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