Validity of the NSO approach beyond leading order

Determine whether Zubarev’s non-equilibrium statistical-operator approach remains valid beyond leading order in the weak charge-violation parameter, and whether the ambiguity in constructing the non-equilibrium operator affects higher-order relaxation-rate predictions.

Background

The paper derives the relaxation law and rate at leading nontrivial order in the weak charge-violation parameter. It notes that alternative but apparently equally justified definitions of the LEQ operator differ at next-to-leading order, leading to distinct NLO contributions in the resulting NEQ operator.

The unresolved issue is whether this construction ambiguity is merely a parametrization artifact or instead changes physical higher-order predictions. The authors specifically state that the validity of the NSO approach beyond leading order is not established.

References

As a word of caution, however, it remains unclear whether the NSO approach is valid beyond leading order in \lambda, as we have touched upon in section~\ref{sec:ZubarevDiscussion}. Since the construction of the NEQ operator appears to be ambiguous at NLO, it is unclear whether this ambiguity also affects higher-order predictions.

— On the relaxation dynamics of non-equilibrium quantum systems  (2609.17447 - Carosi et al., 15 Sep 2026) in Section 3, subsection “Linearized near-equilibrium dynamics,” footnote following equation (3.??) / equation “Relaxation_Gamma_Full”