Wave thermalization and its implications for nonequilibrium statistical mechanics

TL;DR

This paper introduces the concept of wave thermalization, showing that wave scattering in complex media can produce universal nonequilibrium steady states, offering new insights into statistical mechanics at the individual system level.

Contribution

It demonstrates that wave scattering eigenstates lead to universal steady states, proposing wave thermalization as a new principle in nonequilibrium statistical mechanics.

Findings

Universal diffusive steady state emerges from wave eigenstates.

Wave scattering can simulate nonequilibrium thermal environments.

Wave thermalization links wave behavior to macroscopic nonequilibrium phenomena.

Abstract

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.