Emergent universal statistics in nonequilibrium systems with dynamical scale selection

TL;DR

This paper develops a universal statistical framework for nonequilibrium systems with inherent length-scale selection, confirmed through experiments and simulations, advancing the understanding of pattern dynamics across various physical and biological systems.

Contribution

It introduces a universal nonequilibrium distribution for kinetic observables in systems with scale selection, supported by spectral analysis and validated experimentally and numerically.

Findings

Confirmed energy distributions in Faraday surface waves

Validated predictions in active turbulence simulations

Proposed a unified statistical description for pattern-forming systems

Abstract

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 random scattering 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.