The problem arises as KBIs are only defined for infinite systems . In infinite systems, the theoretical long-r limit of the RDF is 1. This means, that for the integrals in eqs. 3, 4, and 6, when the RDF has converged to this limit at some distance r = R, we can safely truncate the integral at R, since the integrand above this R will be 0. However, the limit of the RDF when sampled in a finite-size system of N particles, even if periodic, becomes different from 1. As an example of this, statistical mechanics analysis show that for an ideal gas system, g(r) = 1 -(1/N ) .