  We study fluctuations of the empirical processes of a non-equilibrium
interacting particle system consisting of two species over a domain that is
recently introduced in [8] and establish its functional central limit theorem.
This fluctuation limit is a distribution-valued Gaussian Markov process which
can be represented as a mild solution of a stochastic partial differential
equation. The drift of our fluctuation limit involves a new partial
differential equation with nonlinear coupled term on the interface that
characterized the hydrodynamic limit of the system. The covariance structure of
the Gaussian part consists two parts, one involving the spatial motion of the
particles inside the domain and other involving a boundary integral term that
captures the boundary interactions between two species. The key is to show that
the Boltzmann-Gibbs principle holds for our non-equilibrium system. Our proof
relies on generalizing the usual correlation functions to the join correlations
at two different times.
