In 1966, Félix Izrailev and Boris Chirikov proposed that the system will thermalize, if a sufficient amount of initial energy is provided. The idea here is that the non-linearity changes the dispersion relation, allowing resonant interactions to take place that will bleed energy from one mode to another. A review of such models can be found in Roberto Livi et al. Yet, in 1970, Joseph Ford and Gary H. Lunsford insist that mixing can be observed even with arbitrarily small initial energies. There is a long and complex history of approaches to the problem, see Thierry Dauxois (2008) for a (partial) survey.