  We study the behavior of stationary non-equilibrium two-body correlation
functions for Diffusive Systems with equilibrium reference states (DSe). We
describe a DSe at the mesoscopic level by $M$ locally conserved continuum
fields that evolve through coupled Langevin equations with white noises. The
dynamic is designed such that the system may reach equilibrium states for a set
of boundary conditions. In this form, we make the system driven to a
non-equilibrium stationary state by changing the equilibrium boundary
conditions. We decompose the correlations in a known local equilibrium part and
another one that contains the non-equilibrium behavior and that we call {\it
correlation's excess} $\bar C(x,z)$. We formally derive the differential
equations for $\bar C$. To solve them order by order, we define a perturbative
expansion around the equilibrium state. We show that the $\bar C$'s first-order
expansion, $\bar C^{(1)}$, is always zero for the unique field case, $M=1$.
Moreover $\bar C^{(1)}$ is always long-range or zero when $M>1$. Surprisingly
we show that their associated fluctuations, the space integrals of $\bar
C^{(1)}$, are always zero. Therefore, fluctuations are dominated by local
equilibrium up to second-order in the perturbative expansion around the
equilibrium. We derive the behaviors of $\bar C^{(1)}$ in real space for
dimensions $d=1$ and $2$ explicitly. Finally, we derive the two first
perturbative orders of the correlation's excess for a generic $M=2$ case and a
hydrodynamic model.
