Roughening of two-dimensional interfaces in nonequilibrium phase-separated systems

I show that nonequilibrium two-dimensional interfaces between three-dimensional phase separated fluids ex-hibit a peculiar "sublogarithmic" roughness. Specifically, an interface of lateral extent L will fluctuate vertically (i.e., normal to the mean surface orientation) a typical rms distance w equivalent to root <|h(r, t )|> proportional to [ln (L/a)](1/3) [where a is a microscopic length, and h(r, t) is the height of the interface at two-dimensional position r at time t]. In contrast, the roughness of equilibrium two-dimensional interfaces between three-dimensional fluids, obeys w proportional to [ln (L/a)](1/2). The exponent 1/3 for the active case is exact. In addition, the characteristic timescales tau(L) in the active case scale according to tau(L) proportional to L-3[ln (L/a)](1/3), in contrast to the simple tau(L) proportional to L-3 scaling found in equilibrium systems with conserved densities and no fluid flow.