  As a simple model for single-file diffusion of hard core particles we
investigate the one-dimensional symmetric exclusion process. We consider an
open semi-infinite system where one end is coupled to an external reservoir of
constant density $\rho^\ast$ and which initially is in an non-equilibrium state
with bulk density $\rho_0$. We calculate the exact time-dependent two-point
density correlation function $C_{k,l}(t)\equiv <n_k(t)n_l(t)>-
<n_k(t)><n_l(t)>$ and the mean and variance of the integrated average net flux
of particles $N(t)-N(0)$ that have entered (or left) the system up to time $t$.
We find that the boundary region of the semi-infinite relaxing system is in a
state similar to the bulk state of a finite stationary system driven by a
boundary gradient. The symmetric exclusion model provides a rare example where
such behavior can be proved rigorously on the level of equal-time two-point
correlation functions. Some implications for the relaxational dynamics of
entangled polymers and for single-file diffusion in colloidal systems are
discussed.
