Characterize all entropic inequalities

Characterize the complete set of linear inequalities satisfied by all entropic polymatroids.

Background

The paper uses the Zhang–Yeung inequality to derive an upper bound for the entropic width. It notes that this inequality is only one member of the broader family of information inequalities governing entropic polymatroids.

A complete characterization of these inequalities would clarify the entropic cone and could potentially improve bounds such as the unresolved exact entropic width in the constructed graph.

References

We note that no general characterization of all entropic inequalities is known.

— Separating Notions of Graph Width: the Adaptive, Normal, Linear, Entropic, and Submodular Width  (2609.40018 - Lanzinger et al., 30 Sep 2026) in Section 4, subsection “Inequalities in $\bar \Gamma_n^*$”