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Accepted · first revision · record

Title: Role of Toda integrals in the FPUT metastable state
Plain: The FPUT chain is close to the Toda chain, a solvable model with as many conserved quantities as particles. The question is whether the long-lived non-thermal state of FPUT is the equilibrium of the Toda chain, and how fast its conserved quantities drift.
Precise: Determine whether the pre-thermal state of the $\alpha$-FPUT chain at small $\epsilon$ is described by a generalized Gibbs ensemble built from Toda integrals, and find the scaling with $\epsilon$ and $N$ of the drift time of these integrals, which sets $T_{\mathrm{eq}}$. An answer is a mechanism with a scaling law consistent with simulations.
Settled by: Simulations tracking all Toda integrals in FPUT dynamics, with their drift rates derived from perturbation theory around Toda.
Kind: well-posed
Answer type: mechanism
References: (empty)
Literature status: partially-resolved
Status note: Simulations using Toda integrals as slowly varying quantities support this picture (arXiv:2511.08149, 2025); reported scaling exponents differ between studies.
Posed since: (empty)