We introduce a family of stationary coupled Sasamoto-Spohn models and show that, in the weakly asymmetric regime, they converge to the energy solution of coupled Burgers equations. Moreover, we show that any system of coupled Burgers equations satisfying the so-called trilinear condition ensuring stationarity can be obtained as the scaling limit of a suitable system of coupled Sasamoto-Spohn models.The core of our proof, which avoids the use of spectral gap estimates, consists in a second order Boltzmann-Gibbs principle for the discrete model.

We introduce a family of stationary coupled Sasamoto-Spohn models and show that, in the weakly asymmetric regime, they converge to the energy solution of coupled Burgers equations.Moreover, we show that any system of coupled Burgers equations satisfying the so-called trilinear condition ensuring stationarity can be obtained as the scaling limit of a suitable system of coupled Sasamoto-Spohn models.The core of our proof, which avoids the use of spectral gap estimates, consists in a second order Boltzmann-Gibbs principle for the discrete model. Contents 1. Introduction, model and results 1.1. Coupled Burgers equations 1.2. Coupled Sasamoto-Spohn models and main result 1.3. Structure of the article 1.4. General Notations 2. Energy Solutions of the coupled stochastic Burgers equation 3. Coupled Sasamoto-Spohn Processes 3.1. The Generator and the invariant measure 3.2. The Martingale Decomposition 4. Dynamical Estimates 4.1. The Kipnis-Varadhan estimate 4.2. The one-block estimates 4.3. The second order Boltzmann-Gibbs principle 5. Tightness