Additive functionals of exclusion processes from non-equilibrium

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].
Comment: The main result of this paper is extended from occupation time to additive functionals. The title is changed. More details are added