  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., $T_{eq}\sim \epsilon^{-2}$, where the perturbation
strength, $\epsilon$, 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.
