  We rigorously derive non-equilibrium space-time fluctuation for the particle
density of a system of reflected diffusions in bounded Lipschitz domains in
$\mathbb R^d$. The particles are independent and are killed by a time-dependent
potential which is asymptotically proportional to the boundary local time. We
generalize the functional analytic framework introduced by Kotelenez [19, 20]
to deal with time-dependent perturbations. Our proof relies on Dirichlet form
method rather than the machineries derived from Kotelenez's sub-martingale
inequality. Our result holds for any symmetric reflected diffusion, for any
bounded Lipschitz domain and for any dimension $d\geq 1$.
