  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.
