We define, for wave turbulence, probability density functions (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 (d/dt)∫ρln ρdV is well defined and plays an important role in the system's evolution and we find its representation in the wave turbulence approximation.
|Original language||English (US)|
|Journal||Journal of Statistical Mechanics: Theory and Experiment|
|State||Published - Oct 2004|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty