Forecast long‑time OTOC behavior from finite‑time observations

Determine whether a general, model‑independent procedure exists to extrapolate from finite‑time observations of out‑of‑time‑ordered correlators of few‑body observables to rigorous long‑time (or infinite‑time) predictions of pure‑state thermalization in autonomous unitary (Hamiltonian) many‑body dynamics; either construct such a procedure or prove that no such general procedure exists.

Background

The paper develops a method to establish pure‑state quantum thermalization without statistical averages using out‑of‑time‑ordered correlators (OTOCs). Unlike earlier autocorrelator‑based results that allow extrapolation from finite‑time observations to long‑time conclusions for second‑order correlators, the present OTOC‑based framework yields constraints only at the observed times.

The authors explain that their prior autocorrelator results provide long‑time forecasts from short‑time data in autonomous dynamics, but a corresponding accessible, system‑independent extrapolation for OTOCs is missing. They explicitly note that it is not clear whether such forecasts are possible in general and suggest identifying a method (or proving impossibility) as an outstanding issue. This challenge is also connected to Appendix A.3, which argues that straightforward extensions of earlier techniques do not yield useful long‑time bounds for fourth‑order correlators.

References

When applied to OTOCs, it is not clear that such forecasts are generally possible even in principle (see Appendix~\ref{app:correlators_examples} for details).

— Provable quantum thermalization without statistical averages  (2604.02417 - Vikram, 2 Apr 2026) in Section 5.3

However, the lack of an implication that can extrapolate to energy eigenstates and infinite times (e.g. the second row of the template~eq:thermalizationimplicationtemplate) appears to be a significant open problem for deciding whether general system-independent computational modes of predicting quantum thermalization for arbitrarily long times from finite-time data are even possible, as opposed to system-specific calculations of OTOC factorization (which may extrapolate to long times in specific classes of systems).

— Aperiodicity is sufficient for macroscopic thermalization  (2608.13462 - Vikram, 13 Aug 2026) in Section 5, subsection “Probes, mechanisms, and predictions,” paragraph “Microscopic quantum thermalization”