A method for testing the cosmic homogeneity with Shannon entropy

We propose a method for testing cosmic homogeneity based on the Shannon entropy in Information theory and test the potentials and limitations of the method on Monte Carlo simulations of some homogeneous and inhomogeneous 3D point process in a finite region of space. We analyze a set of N-body simulations to investigate the prospect of determining the scale of homogeneity with the proposed method and show that the method could serve as an efficient tool for the study of homogeneity.