  Non-Gibbsian stationary states occur in dissipative non-equilibrium systems.
They are closely connected with the lack of detailed balance and the absence of
a fluctuation-dissipation theorem. These states exhibit spatial correlations
that are long ranged under generic conditions, even in systems with short range
interactions, provided the system has slow modes and some degree of spatial
anisotropy. In this paper we present a theory for static pair correlations in
lattice gas automata violating detailed balance, and we show that the spatially
uniform non-Gibbsian equilibrium state exhibits long range correlations, even
in the absence of an external driving field.
