This segment explores deterministic processes within spacetimes containing closed timelike curves (CTCs), which permit backwards time travel. The authors extend a previous framework, the process matrix formalism, to an arbitrary number of spacetime regions, showing that complex, consistent dynamics are possible with CTCs. They define and characterise process functions, proving that while local operations within regions are freely chosen, inter-regional signalling remains conditionally one-way to prevent paradoxes. Examples of quadripartite processes, impossible without CTCs, illustrate the richness of these non-causally ordered dynamics. The paper concludes that CTCs are compatible with determinism, free choice, and the absence of inconsistencies.

Original study: https://iopscience.iop.org/article/10.1088/1361-6382/aba4bc