Reversible dynamics in strongly non-local Boxworld systems

In order to better understand the structure of quantum theory, or speculate about theories that may supersede it, it can be helpful to consider alternative physical theories. 'Boxworld' describes one such theory, in which all non-signaling correlations are achievable. In a limited class of multipartite Boxworld systems - wherein all subsystems are identical and all measurements have the same number of outcomes - it has been demonstrated that the set of reversible dynamics is 'trivial', generated solely by local relabellings of measurement choices and outcomes, and permutations of subsystems. We develop the convex formalism of Boxworld to give an alternative proof of this result, then extend this proof to all multipartite Boxworld systems, and discuss the potential relevance to other theories. These results lend further support to the idea that the rich reversible dynamics in quantum theory may be the key to understanding its structure and its informational capabilities.