  A scalar model of wet active matter in the presence of an imposed temperature
gradient, or chemical potential gradient, is considered. It is shown that there
is a convective instability driven by a (negative) activity parameter. In this
non-equilibrium steady state the generic long-ranged correlations are computed
and compared and contrasted with the analogous results in a passive fluid. In
addition, the non-equilibrium Casimir pressure or force is computed.
Singularities in various physical quantities as the instability is approached
are determined. Finally, we give the generalized Lorenz equations
characterizing the fluid behavior above the instability and contrast these
equations to the Lorenz equations for the Rayleigh-Bernard instability in a
passive fluid.
