Thermodynamics of classical integrable field theories

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.