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

We propose and demonstrate, with the one-dimensional Korteweg-de Vries-Burgers model, the scenarios of transfer loop and $\mathit{\text{all-scale}}$ 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.