Quantifying Nonequilibrium Behavior with Varying Cooling Rates

We investigate nonequilibrium behavior in (1+1)-dimensional stochastic field theories in the context of Ginzburg-Landau models at varying cooling rates. We argue that a reliable measure of the departure from thermal equilibrium can be obtained from the absolute value of the rate of change of the momentum-integrated structure function, $\Delta S_{\rm{tot}}$. We show that the peak of $\Delta S_{\rm{tot}}$ scales with the cooling, or quench, time-scale, $\tau_q$, in agreement with the prediction by Laguna and Zurek for the scaling of freeze-out time in both over and under-damped regimes. Furthermore, we show that the amplitude of the peak scales as $\tau_q^{-6/5}$ independent of the viscosity.