Transfer Loop and Statistical Equilibrium of Korteweg-de Vries-Burgers Systems Associated to Classical Nonlinear Acoustics and Quantum Shock Waves

TL;DR

This paper explores the transfer loop and statistical equilibrium in Korteweg-de Vries-Burgers systems, linking shock formation and Gaussian distributions, with implications for nonlinear acoustics and quantum shock wave experiments.

Contribution

It introduces the concepts of transfer loop and all-scale statistical equilibrium in Korteweg-de Vries-Burgers models, connecting shock dynamics to statistical mechanics.

Findings

Identification of transfer loop scenarios related to shock formation

Demonstration of all-scale statistical equilibrium with wavelength-dependent temperatures

Potential for experimental testing in nonlinear acoustics and quantum shock waves

Abstract

We propose and demonstrate, with the one-dimensional Korteweg-de Vries-Burgers model, the scenarios of transfer loop and \textit{all-scale} statistical equilibrium, the former being associated to shock formation and the latter to Gaussian distributions as in a canonical ensemble, but with wavelength-dependent temperatures. The discussions emphasize, among the multi-disciplinary relevance, the classical nonlinear acoustics and quantum shock waves, for the possibility of more favorable experimental tests.