Theorem. The properties of these terms, especially up through the 4 ∆ with their role in establishing N -Representability criteria for the reconstruction of the 2-RDM, have been well-reviewed in the literature and have been explicitly connected to other quantities such as CC amplitudes. As in traditional statistical theory, in which the first-order cumulant is identical to the mean, the 1 ∆ is identical to the 1 Γ and yields no additional unique information over the above quantity. As the lowest unique quantity, of particular interest among these is the cumulant of the 2-RDM, which is defined in terms of the 2-RDM and the 1-RDM ( 1 Γ):