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Wet active matter in the presence of an imposed temperature gradient, orchemical potential gradient, is considered. It is shown that there is a newtype of convective instability that is caused by a (negative) activityparameter. Physically this corresponds to active fluids with contractualstress. In this non-equilibrium steady state the singular generic long-rangedcorrelations are computed and compared with the analogous results in a passivefluid. In addition, the singular non-equlibirum Casimir pressure or force isdetermined. The fluid motion above the instability is determined bygeneralizing the Lorenz equations for the Rayleigh-Benard instability in apassive fluid to Lorenz-like equations to describe this new instability.

Driven active matter: fluctuations and a hydrodynamic instability