Invariant measures and entropy production in wave turbulence

Abstract

We define, for wave turbulence, probability density functions ρ (pdfs) on a suitably chosen phase space. We derive the Liouville equation for their evolution and identify their long time behaviours corresponding to equipartition and finite flux Kolmogorov–Zakharov (KZ) spectra. We demonstrate that, even in nonisolated systems, entropy production is well defined and plays an important role in the system's evolution and we find its representation in the wave turbulence approximation.