Classical information entropy of parton distribution functions and an application in searching gluon saturation

Entropy or information is a fundamental quantity contained in a system in statistical mechanics and information theory. In this paper, a definition of classical information entropy of parton distribution functions is suggested. The extensive and supper-additive properties of the defined entropy are discussed. The concavity is also deduced for the defined entropy. As an example, the classical information entropy of the gluon distribution of the proton is presented. There are some particular features of the evolution of the information entropy in the saturating domain, which could be used in finding the signals of gluon saturation.