Cooling rate and glassy behavior in the Fermi--Pasta--Ulam system

In this work, we numerically studied the cooling process of a Fermi--Pasta--Ulam system, which occurs when the FPU system is placed in contact with a gas whose temperature $T$ is reduced with a certain cooling rate $\xi$. It was found that the existence of a weak stochastic threshold has a significant impact on the cooling process, because below such a stochastic threshold the specific FPU energy is larger than its temperature, i.e., the FPU system falls out of equilibrium. The difference remains finite in the limit $T \to 0$, so that the FPU system maintains a residual amount of energy $E_0$ at vanishing temperature. Our numerical simulations reveal that this energy exhibits a power--law dependence on both the system size and the cooling rate, scaling approximately as $E_{0} \sim (\xi N)^{2/3}$.