Surface Critical Behavior in Systems with Absorbing States

We present a general scaling theory for the surface critical behavior of non-equilibrium systems with phase transitions into absorbing states. The theory allows for two independent surface exponents which satisfy generalized hyperscaling relations. As an application we study a generalized version of directed percolation with two absorbing states. We find two distinct surface universality classes associated with inactive and reflective walls. Our results indicate that the exponents associated with these two surface universality classes are closely connected.