State reachability under a bounded non-Markovianity budget

Determine which electronic population states remain accessible in the molecular photoswitch model when the degree of non-Markovianity, quantified by the Rivas–Huelga–Plenio (RHP) measure, is constrained below a fixed threshold.

Background

The paper studies a four-level molecular photoswitch coupled to structured vibrational environments represented by damped pseudomodes. Its numerical results indicate that environmental memory can enlarge the set of population transformations accessible to the reduced electronic system, including transformations that are inaccessible under Markovian thermal dynamics. However, the magnitude of non-Markovianity alone does not determine whether the dynamics approaches the optimal thermal-operation bound; the coupling architecture and population-transfer pathways are also important.

The authors therefore identify a more refined unresolved problem: characterize the reachable states when non-Markovianity is treated as a limited resource. Specifically, the RHP measure would serve as a memory budget, and the task is to determine how the accessible region changes as that budget is fixed or bounded. This would quantify the trade-off between allowed environmental memory and dynamical state reachability beyond the yield optimization considered in the paper.