  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 far-from-equilibrium dynamics and
statistics poses major conceptual and practical challenges due to the absence
of energy and momentum conservation laws. Here, we experimentally and
theoretically investigate the statistics of prototypical nonequilibrium systems
in which inherent length-scale selection confines the dynamics near a mean
energy hypersurface. Guided by spectral analysis of the field modes and scaling
arguments, we derive a universal nonequilibrium distribution for kinetic field
observables. We confirm the predicted energy distributions in experimental
observations of Faraday surface waves, 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, suggesting a path towards a unified
statistical field theory of nonequilibrium systems with length-scale selection.
