  We consider single-file diffusion in an open system with two species $A,B$ of
particles. At the boundaries we assume different reservoir densities which
drive the system into a non-equilibrium steady state. As a model we use an
one-dimensional two-component simple symmetric exclusion process with two
different hopping rates $D_A,D_B$ and open boundaries. For investigating the
dynamics in the hydrodynamic limit we derive a system of coupled non-linear
diffusion equations for the coarse-grained particle densities. The relaxation
of the initial density profile is analyzed by numerical integration. Exact
analytical expressions are obtained for the self-diffusion coefficients, which
turns out to be length-dependent, and for the stationary solution. In the
steady state we find a discontinuous boundary-induced phase transition as the
total exterior density gradient between the system boundaries is varied. At one
boundary a boundary layer develops inside which the current flows against the
local density gradient. Generically the width of the boundary layer and the
bulk density profiles do not depend on the two hopping rates. At the phase
transition line, however, the individual density profiles depend strongly on
the ratio $D_A/D_B$. Dynamic Monte Carlo simulation confirm our theoretical
predictions.
