  We investigate the thermodynamics of integrable classical field theories
under the effect of a random initial configuration, motivated by the
nonequilibrium evolution of quantum field theories. The approach to thermal
equilibrium is analysed with numerical simulations and confronted with
analytical results. The possibility of comparing the classical results with
their quantum counterparts could be a way of inferring the behaviour of
out-of-equilibrium quantum field theories during the thermalization process.

Statistical Mechanics