  We consider the effect of uniform driving on the interface between two phases
which are described by model C dynamics. The non-driven system has a classical
Gaussian interface described by capillary wave theory. The model under driving
retains Gaussian statistics but the interface statistics are modified by
driving, notably the height fluctuations are suppressed and the correlation
length of the fluctuations is increased. The model we introduce can also be
used as a model for the effect of activity on interface dynamics.
