Introduction to Mathematical Physics/Statistical physics/Exercise

Exercice:

Consider a chain of $N$ nonlinear coupled oscillators. Assuming known the (deterministic) equation governing the dynamics of the particles, is that possible to define a system's temperature? Can one be sure that a system of coupled nonlinear oscillators will evolve to a state well described by statistical physics? Do a bibliographic research on this subject, in particular on Fermi--Ulam--Pasta model.