Things moving in one direction wouldn’t preclude the existence of cycles.

For example: a language has noun cases -> phonological changes cause the endings to merge together, requiring prepositions to disambiguate -> prepositions become more tightly bound to the words they modify and are eventually reanalyzed as case markings. Now we’re back with cases even if languages can only take each step in the given direction.

> Incidentally Chinese did not evolve from Proto-Indo-European.

You’re right, but I meant to imply that PIE is the oldest language whose grammar we know a lot about, not that it’s the ancestor of every modern language.

Mind blowing paper: Chang, T. T.(1988). Indo-European vocabulary in Old Chinese: A new thesis on the emergence of Chinese language and civilization in the Late Neolithic Age. In Sino-Platonic Papers eds Mair, V. http://sino-platonic.org/complete/spp007_old_chinese.pdf

I'm don't know enough about Indo-European reconstructions to make my own opinions on what's exposed on the this side and the paper is a bit dated but examples are very compelling.

I'm not convinced at all by that paper, he gives only by my count ~180 examples to relate two language families that by themselves have 10s of thousands morphemes. Especially since the reconstructed Indo-European rootwords and Ancient Chinese pronounciations are themselves dubious. I suspect you could probably get correlation of this level with pretty much any two language families taken at random.