Hyperuniform interfaces in non-equilibrium phase coexistence

We show that long-wavelength interfacial fluctuations are strongly suppressed in non-equilibrium phase coexistence between bulk hyperuniform systems. Using simulations of three distinct microscopic models, we demonstrate that hyperuniform interfaces are much smoother than equilibrium ones, with a universal reduction of height fluctuations at large scale. We derive a non-equilibrium interface equation from the field theory of the bulk order parameter, and predict a reduction in height fluctuations, $S_h(\mathit{k})\equiv ⟨\mathrm{\mid }h(\mathit{k}){\mathrm{\mid }}^2⟩\sim \mathrm{\mid }\mathit{k}{\mathrm{\mid }}^{-1}$, in stark contrast to equilibrium capillary wave theory where $S_h(\mathit{k})\sim \mathrm{\mid }\mathit{k}{\mathrm{\mid }}^{-2}$. Our results establish a new universality class for non-equilibrium interfaces, highlighting the fundamental role of suppressed bulk fluctuations in shaping interfacial dynamics far from equilibrium.