In special cases, (N = 2 any λ and λ → ∞ for any N ), there is a one-to-one correspondence between σ λ i (r) and w λ (r). For these special cases, one can use the exact w λ (r) (available for small systems), translate it to 'exact' σ λ i (r), and then use those to guide the improvement of MRF. In general, there is no one-to-one correspondence between σ λ i (r) and w λ (r). This is circumvented within the so-called the reversed MRF machinery (rm-MRF), where one approximates σ λ i (r) by σλ (r), which is the constant, i-averaged fluctuation function. With this approximation, we get a one-to-one correspondence between σλ (r) and w λ (r):