From absolute equilibrium to Kardar–Parisi–Zhang crossover: A short review of recent developments

I first recall the theoretical background relevant to spectral truncation: absolute equilibrium in helical flows and compressible effects. Thermalization phenomenology in Gross–Pitaevskii superflows and thermalization processes in classical systems are then briefly reviewed. The so-called ’tygers’ that appear in the truncated inviscid Burgers equation are demonstrated. The basic definitions that relate the Burgers equation to the Kardar–Parisi–Zhang system are recalled. Spectral truncation and conserved quantities are used to introduce the microcanonical and canonical stationary probabilities. The main results on the crossover from absolute equilibrium to Kardar–Parisi–Zhang scaling are finally given after a brief discussion of the relevant physical parameters. The present contribution is thus a short review of the publications, scientific developments and collaborations that went on during the last decade and led to the joint work (Cartes et al., 2022) that I presented at the XVIII Instabilities and Nonequilibrium Structures Workshop held (online) in December 2021 in Valparaiso (Chile), dedicated to the memory of the late Enrique Tirapegui.