  Consider the weakly asymmetric simple exclusion processes on the
one-dimensional torus. We study the non-equilibrium fluctuation of a class of
additive functionals, and show that its scaling limit is a Gaussian process.
The proof is mainly based on the results obtained and techniques developed by
Jara and Menezes [Non-equiliburim fluctuations of interacting particle systems,
arXiv:1810.09526].
