Coarsening in (nearly) mass-conserving two-component reaction diffusion systems

We show that coarsening in two-component mass-conserving reaction-diffusion systems is driven by self-amplifying mass transport between neighboring high-density domains. We derive a general coarsening criterion and provide a geometric argument, independent of the specific reaction kinetics, to show that coarsening is generically uninterrupted, confirming a long-standing hypothesis in the field. The theory is then generalized to study interrupted coarsening and anti-coarsening (domain splitting) for systems with weakly broken mass conservation, providing a path to analyze length scale selection in pattern formation far from equilibrium.