Holographic entropy inequalities pass the majorization test

TL;DR

This work investigates whether holographic entropy inequalities, originally proven for time-reversal symmetric (static) settings via minimal-cut constructions, extend to time-dependent scenarios. It formalizes the majorization test and develops a contraction-map framework that proves two key properties: (i) every null reduction of a balanced holographic inequality passes the majorization test, and (ii) every null reduction of a superbalanced inequality remains a valid holographic inequality. These results yield a Main Corollary linking overlaps of LHS and RHS terms under contractions and several further corollaries, strengthening the link between static entropy constraints and dynamical bulk geometry, including connections to quantum erasure correction and the holographic RG. The paper also discusses the broader interpretive implications for dynamics in holographic theories and notes concurrent work that refines the landscape of these inequalities. A contemporaneous note acknowledges overlaps with another draft that challenges some converse statements, outlining directions for future synthesis and interpretation.

Abstract

Quantities computed by minimal cuts, such as entanglement entropies achievable by the Ryu-Takayanagi proposal in the AdS/CFT correspondence, are constrained by linear inequalities. We prove a previously conjectured property of all such constraints: Any $k$ systems on the "greater-than" side of the inequality are subsumed in some $k$ systems on its "less-than" side (accounting for multiplicity). This finding adds evidence that the same inequalities also constrain the entropies under time-dependent conditions because it preempts a large class of potential counterexamples. We prove several other properties of holographic entropy inequalities and comment on their relation to quantum erasure correction and the Renormalization Group.