comparison of proton structure functions in classical and quantum viewpoints

A comparison between quantum statistical parton distributions and the classical perspective in proton is presented. the structure functions and parton distributions are only provided by the entropy maximization principle and proton sum rules. in both the classical and quantum approaches, the equations for the number of proton valence quarks, conservation of momentum, and the first and second laws of thermodynamics are satisfied. however, if we use the maxwell-boltzmann distribution function to describe the partons in the proton structure function, the results show a clear deviation from the experimental results, while the fermi-dirac and bose-einstein distributions are in good agreement with the measurements from accelerators.