  Understanding the rich spatial and temporal structures in nonequilibrium
thermal environments is a major subject of statistical mechanics. Because
universal laws, based on an ensemble of systems, are mute on an individual
system, exploring nonequilibrium statistical mechanics and the ensuing
universality in individual systems has long been of fundamental interest. Here,
by adopting the wave description of microscopic motion, and combining the
recently developed eigenchannel theory and the mathematical tool of the
concentration of measure, we show that in a single complex medium, a universal
spatial structure - the diffusive steady state - emerges from an overwhelming
number of scattering eigenstates of the wave equation. Our findings suggest a
new principle, dubbed "the wave thermalization", namely, a propagating wave
undergoing complex scattering processes can simulate nonequilibrium thermal
environments, and exhibit macroscopic nonequilibrium phenomena.
