Monte Carlo and deterministic calculation of the mutual information of the fission source in k-eigenvalue calculations

The mutual information, a quantity measuring the dependency of two random variables, is studied in the context of the fission source of neutron transport calculations. Both Monte Carlo and integral transport methods are developed to compute the mutual information in 1-D and 2-D Cartesian geometry. The mutual information of the fission source may be connected to the correlation of fission sources of different iterations within a Monte Carlo calculation and the resulting underestimation of tally uncertainties. Results suggest that a reasonable global correction of tally uncertainties may be obtained. The calculations demonstrate the Monte Carlo estimate of the mutual information has a positive bias that is proportional to the square of the number of discrete regions divided by the number of active histories, agreeing with theoretical behavior. This asymptotic form may be used to get a reasonable estimate of the mutual information of the fission source in Monte Carlo calculations.