Ensemble dynamics of a classical relativistic non-integrable model

We study quench dynamics and relaxation in relativistic field theories models and give evidence that non-

integrable models do not relax to the thermal ensemble. The information content of the equilibrium state that

emerges at large times after a quench is generally expected to be related to the number of extensive (local and

quasi-local) conserved charges of the Hamiltonian describing the dynamics. In integrable models the equilibrium

state is therefore a Generalised Gibbs Ensemble where each extensive charge enters with an independent Lagrange

multiplier. In non-integrable models this ensemble is expected to reduce to the standard Gibbs ensemble since the

Hamiltonian is the only extensive charge. The mechanism that is responsible for the emergence of such equilibrium

states is believed to be the scrambling of initial state information due to the delocalisation induced by the dynamics

and the fact that initial information originating from spatially distant points is incoherent (a property that can be

expressed as correlation clustering in the initial state).