Relating information entropy and mass variance to measure bias and non-Gaussianity

We relate the information entropy and the mass variance of any distribution in the regime of small fluctuations. We use a set of Monte Carlo simulations of different homogeneous and inhomogeneous distributions to verify the relation and also test it in a set of cosmological N-body simulations. We find that the relation is in excellent agreement with the simulations and is independent of number density and the nature of the distributions. We show that the relation between information entropy and mass variance can be used to determine the linear bias on large scales and detect the signatures of non-Gaussianity on small scales in galaxy distributions.