Why Quasi-equilibrium, Quasi-stationary and Pre-thermalization phases are related - Relaxation in strongly nonlinear systems

In 2004, we introduced the concept of the quasi-equilibrium state in strongly nonlinear classical many particle systems. Later in the same year, Berges et al introduced a similar state and named it pre-thermalization. In recent experiments, this state, also called the quasi-stationary state, has been reported. We will discuss the properties of the quasi-equilibrium phase for the Fermi-Pasta-Ulam-Tsingou and Hertz systems and how equipartitioning can set in from the quasi-equilibrium state.