Mechanical structures inside proton with configurational entropy language

The structure of the proton remains a significant challenge within the field of Quantum Chromodynamics, with the origin of its spin and mass still lacking a satisfactory explanation. In this study, we utilize the gravitational form factor of the proton as the foundation for constructing the configurational entropy of the proton energy system. In our approach we choose the holographic QCD model for input thus obtaining a holographic version of the proton energy density. Employing this approach, we are able to determine key mechanical quantities such as the proton's mass radius and pressure distribution. Our analysis yields the root-mean-square mass radius of $\sqrt{\langle r_M^2\rangle}=0.720$ fm and scalar radius of $\sqrt{\langle r_S^2\rangle}=1.024$ fm for proton, which are found to be in excellent agreement with recent measurements from the Hall-C collaboration group at Jefferson Lab. Additionally, we examine the radial distribution of pressure and shear force within the proton. We provide a new mode for constraining holographic model parameters in the investigation of proton structures.