We obtain an analytic relation between the information entropy and the variance of a 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. The relation would help us to relate entropy to other conventional measures and widen its scope.
Tue, 12 Jul 16
Comments: 5 pages, 2 figures, Submitted to MNRAS, Comments are welcome. arXiv admin note: substantial text overlap with arXiv:1301.4961