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

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