Continuum theories of active phase separation: Recent developments

To study phase separation in conventional binary fluids one posits a phi-4 free energy functional and sets up a model whereby the particle current is proportional to the gradient of chemical potential (plus noise). This is Model B. Alternatively, in Model H, one couples this to a conserved momentum field, representing fluid velocity. In either case, the model respects detailed balance and exhibits time reversal symmetry (TRS) in steady state. In active systems, particles such as bacteria or self-propelled colloids perform motions that locally break detailed balance: time reversal symmetry is broken because their steady-state entropy production is nonzero locally. I will present extensions of Model B (and briefly, if time allows, Model H) that encode this type of TRS breaking via minimal extra terms in the equations of motion. These terms can alter phase boundaries, convert bulk phase separation into pattern formation with a finite length scale, and exhibit interesting RG flows such that a system that lies in the same universality class as Model B nonetheless has steady-state entropy production at criticality that is significant at all length scales.