Nonintegrability is a necessary condition for the thermalization of a generic Hamiltonian system. In practice, the integrability can be broken in various ways. As illustrating examples, we numerically studied the thermalization behaviors of two types of one-dimensional (1D) diatomic chains in the thermodynamic limit. One chain was the diatomic Toda chain whose nonintegrability was introduced by unequal masses. The other chain was the diatomic Fermi-Pasta-Ulam-Tsingou-β chain whose nonintegrability was introduced by quartic nonlinear interaction. We found that these two different methods of destroying the integrability led to qualitatively different routes to thermalization, but the thermalization time, Teq, followed the same law; Teq was inversely proportional to the square of the perturbation strength. This law also agreed with the existing results of 1D monatomic lattices. All these results imply that there is a universal law of thermalization that is independent of the method of breaking integrability.

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The Toda lattice is a nonlinear but integrable system. Here we study the thermalization problem in one-dimensional, perturbed Toda lattices in the thermodynamic limit. We show that the thermalization time, T eq , follows a universal law; i.e. T eq ∼ò −2 , where the perturbation strength, ò, characterizes the nonlinear perturbations added to the Toda potential. This universal law applies generally to weak nonlinear lattices due to their equivalence to perturbed Toda systems.

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