  In order to better understand the structure of quantum theory, or speculate
about theories that may supercede 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 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.
