Page Entropy of Proton System in Deep-Inelastic-Scattering at Small-$x$

Abstract

The partons model reveals the dynamical structure of nucleons (protons and neutrons). Studies related to thermodynamic quantities of nucleons are interesting and topical questions. In this work, for the first time we apply Page's theory of the studies of black hole to investigate the entropy of 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 $S=\ln m-1/2$, 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 DIS measurements from H1 collaboration.

6 pages, 2 figures, Accepted by PRD

References in corpus (17)

• LHAPDF6: parton density access in the LHC precision era
• New Relations for Gauge-Theory Amplitudes
• The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional
• Deep inelastic scattering as a probe of entanglement: confronting experimental data
• Dynamical entropy of dense QCD states
• Evidence for the maximally entangled low $x$ proton in Deep Inelastic Scattering from H1 data
• Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model
• Quantum chromodynamics at high energy and statistical physics
• Quantum information approach to high energy interactions
• Entanglement entropy production in deep inelastic scattering
• Dynamical parton distributions from DGLAP equations with nonlinear corrections
• An Analytical Solution of the Balitsky-Kovchegov Equation with the Homogeneous Balance Method
• On parton number fluctuations at various stages of the rapidity evolution
• Multiplicity distribution of dipoles in QCD from Le, Mueller and Munier equation
• Determination of the entanglement entropy in elastic scattering using model-independent method for hadron femtoscopy
• Exclusive vector meson productions with the analytical solution of Balitsky-Kovchegov Equation
• Spin-glass model of QCD near saturation

Cited by in corpus (4)

• QCD evolution of entanglement entropy
• Entanglement entropy of the proton in coordinate space
• Entanglement as a probe of hadronization
• Classical information entropy of parton distribution functions and an application in searching gluon saturation