Low Q² boundary conditions for DGLAP equations dictated by quantum statistical mechanics

We discuss the role of quantum statistical mechanics in the description of the parton distribution functions in the proton. It provides the low Q ² boundary conditions for DGLAP equations in terms of Fermi–Dirac and Bose–Einstein functions of the fractional momentum variable x. The successful comparison with experimental data on both the unpolarised and polarised deep inelastic structure functions is reviewed. We argue that the statistical approach for the nucleon parton distributions functions has the nice feature that the free model parameters are fixed from data with high statistics and small systematic uncertainties, providing a strong constraint on the information not supplied by the experiments. (paper: disordered systems, classical and quantum)