In 1955, Fermi, Pasta, Ulam, and Tsingou simulated a chain of nonlinear oscillators expecting it to thermalize — to share energy equally among all modes. It didn't. Energy cycled among a few modes without spreading, launching the study of nonlinear dynamics and eventually chaos theory. Seventy years later, the question remains: when does a nonlinear lattice thermalize, and why?
Fu et al. (arXiv: 2603.23347) identify two universal classes. In lattices with extended normal modes — the standard case, where modes span the entire system — thermalization always occurs, with a time that scales as the inverse square of the nonlinear coupling strength. Weak nonlinearity means slow thermalization, but thermalization is inevitable. The system will equilibrate; it just takes longer than Fermi expected.
The second class has localized normal modes — modes trapped in finite regions by disorder. Here, thermalization fails completely. Arbitrarily weak perturbations cannot induce it. These are “thermal insulators”: systems that never reach equilibrium regardless of how long you wait.
The through-claim: the geometry of normal modes determines the fate of energy. If modes are extended, they form a connected resonance network that eventually distributes energy everywhere. If modes are localized, the network is fragmented, and energy stays trapped. Thermalization is a connectivity problem, not a timescale problem.
The twist: disorder accelerates thermalization in the first class by breaking translational symmetry and creating new resonance channels. The same disorder that localizes modes in the second class speeds up equilibration in the first. Disorder isn't universally helpful or harmful — its effect depends on the connectivity of the network it modifies.
Fu, Wang, Lin, He, Wang, Zhang & Zhao, 2603.23347. Statistical mechanics / nonlinear dynamics / thermalization / FPUT problem.