Driven active matter: fluctuations and a hydrodynamic instability

Wet active matter in the presence of an imposed temperature gradient, or chemical potential gradient, is considered. It is shown that there is a new type of convective instability that is caused by a (negative) activity parameter. Physically this corresponds to active fluids with contractual stress. In this non-equilibrium steady state the singular generic long-ranged correlations are computed and compared with the analogous results in a passive fluid. In addition, the singular non-equlibirum Casimir pressure or force is determined. The fluid motion above the instability is determined by generalizing the Lorenz equations for the Rayleigh-Benard instability in a passive fluid to Lorenz-like equations to describe this new instability.