Non-Shannon information in higher-order responses

Determine whether cubic or higher-order shape responses of the six-party holographic entropy functional G_6 retain its non-Shannon coefficient information that is absent from the quadratic response.

Background

The quadratic response of G_6 is forced onto pair susceptibilities controlled by strong subadditivity, even though the finite G_6 inequality is not a nonnegative combination of elemental Shannon inequalities. This leaves open whether genuinely multipartite information appears at higher orders in the deformation amplitude.

The proposed investigation would identify the first response order at which the non-Shannon coefficients of G_6 become detectable, subject to the differentiability and holographic-limit assumptions used throughout the paper.

References

Determining whether any higher response of $G_6$ retains its non-Shannon coefficients would test where genuinely multipartite local information first appears.

— Beyond Strong Subadditivity: Holographic Entropy Inequalities Along Renormalization Group Flows  (2608.25287 - Bao et al., 26 Aug 2026) in Section 5, Conclusions and outlook, item (iii)