An unreviewed preprint posted to arXiv challenges a common implicit assumption in the study of prethermalization: that a separation of energy scales in a Hamiltonian is sufficient to produce a long-lived prethermal regime. The authors argue that this structural property of the Hamiltonian is necessary but not sufficient — under the very same Hamiltonian, certain observables may display a pronounced prethermal plateau while others relax directly toward thermal equilibrium without any intermediate arrest.
The paper identifies the mechanism behind this selectivity, showing that whether a prethermal plateau appears depends jointly on the Hamiltonian, the choice of observable, and the initial state. The analysis is developed in the context of systems near a fully permutation-symmetric limit and is illustrated concretely using a long-range interacting spin model, a class of systems directly relevant to current experimental platforms. The authors also prove a formal bound: the Loschmidt echo — a measure of quantum state distinguishability under time reversal — provides a lower bound on the prethermal lifetime of any bounded observable, provided both the prethermal and exact dynamics are unitary.
If these claims survive peer review, they would refine how theorists diagnose and predict prethermal behavior, particularly in experiments where only a limited set of observables is accessible. The result adds nuance to the growing body of work on quantum thermalization by making the conditions for prethermalization more precise and operationally dependent.