Connection between boundary conditions and the speed of ergodicity breaking

Investigate and quantify how the boundary driving permutation TB influences the site index at which ergodicity breaks (the “speed” of ergodicity breaking) in boundary-driven semi-infinite reversible cellular automata, starting with k=5 and extending to larger k.

Background

The authors observe for k=5 that different boundary permutations can delay or hasten the first site at which ergodicity fails for a given rule, indicating a dependence of the ‘speed’ of ergodicity breaking on the boundary condition.

A systematic theory linking boundary permutations to this speed is lacking and would inform both theoretical understanding and practical verification strategies.