Hydrodynamic limit of a nongradient interacting particle process

A simple example of a nongradient stochastic interacting particle system is analyzed. In this model, symmetric simple exclusion in one dimension in a periodic environment, the dynamical term in the Green-Kubo formula contributes to the bulk diffusion constant. The law of large numbers for the density field and the central limit theorem for the density fluctuation field are proven, and the Green-Kubo expression for the diffusion constant is computed exactly. The hydrodynamic equation for the model turns out to be linear.