  We study the capacity of entanglement as an alternative to entanglement
entropies in estimating the degree of entanglement of quantum bipartite systems
over fermionic Gaussian states. In particular, we derive the exact and
asymptotic formulas of average capacity of two different cases - with and
without particle number constraints. For the later case, the obtained formulas
generalize some partial results of average capacity in the literature. The key
ingredient in deriving the results is a set of new tools for simplifying finite
summations developed very recently in the study of entanglement entropy of
fermionic Gaussian states.
