Emergent universal statistics in nonequilibrium systems with scale selection

Pattern-forming nonequilibrium systems are ubiquitous in nature, from driven quantum matter and biological life forms to atmospheric and interstellar gases. Identifying universal aspects of their dynamics poses major conceptual and practical challenges due to the violation of energy conservation laws. Here, we investigate experimentally and theoretically the statistics of prototypical nonequilibrium systems in which inherent length-scale selection mechanisms confine the dynamics near a known hypersurface. Guided by the spectral analysis of field energies, we discovered generic conditions under which symmetry arguments predict emergent universal statistics even far from equilibrium. We confirmed this prediction in experimental observations of Faraday surface waves on water, and in quantum chaos and active turbulence simulations. Our results indicate that pattern dynamics and transport in driven physical and biological matter can often be described through monochromatic random fields, thus pointing a path to a unified statistical field theory of nonequilibrium systems with length-scale selection.