  We consider a class of interacting particle systems in continuous space of
non-gradient type, which are reversible with respect to Poisson point processes
with constant density. For these models, a rate of convergence was recently
obtained in 10.1214/22-AOP1573 for certain finite-volume approximations of the
bulk diffusion matrix. Here, we show how to leverage this to obtain
quantitative versions of a number of results capturing the large-scale
fluctuations of these systems, such as the convergence of two-point correlation
functions and the Green-Kubo formula.
