Quantifying nonequilibrium behavior with varying quenching rates

We investigate the approach to thermal equilibrium of (1+1)-dimensional stochastic Ginzburg–Landau models at varying cooling rates. The nonequilibrium dynamics is modeled by coupling the field to an external heat bath with damping rate η. We argue that the departure from thermal equilibrium can be measured from the absolute value of the rate of change of the momentum-integrated structure function, Δ(t). If the field equilibration time-scale is faster than the cooling (or quench) time-scale τq, then Δ(t)→0. Otherwise, Δ(t) displays a peak which scales as τqn, with 1/3≤n≤1/2 as η is varied from the underdamped to the overdamped limit. Furthermore, we show that the amplitude of the peak in Δ(t) measures the departure from equilibrium and scales as τq−6/5, independent of η.