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are/were closely linked ( to each other ).

Chinese term (edited): ϢϢ���

"are closely related (to each other)" or
"are closely linked (to each other)"

Chinese term (edited): ϢϢ���

closely interrelated/intertwined/interwoven

Chinese term (edited): ϢϢ���

...

Chinese term (edited): ϢϢ���

【息息相關】呼吸相通。比喻彼此契合無間或關係密切。 清 蔣士銓 《第二碑‧書表》︰“ 昭明太子 爲我撰成墓表，仍求 吳姐 書丹，恰好上仙亦至，可見三人息息相關。”

Chinese term (edited): ϢϢ���

I agree 100% that:
Closely - related, bound up, linked, interrelated, intertwined, interweave are terms cover the basic meaning of息息相关. I perceive the same concept each time I see the term - 息息相关.

But to all of us, as a Chinese language learner and user, native speakers and non-native speakers, can easily agree that there is a bigger picture hidden than those meanings already described in the above English terms. And there may or may not be a single English word or a simple English phrase to point a full picture of what “息息相关” is all about!

息息相关 also means one cannot live fully without the other; like flower and leaves.

息息相关 also means one’s existence will be compromised without the other.

息息相关 also means when “A” thrives, “B” will also be benefited.

Angus’s “cognate” and monxmood’s “intimately …” were attempts pointing to that direction.

It is this “not enough to quench my thirst” feeling, I would like to solicit from the open audience more English terms that can truly “married” to the term “息息相关”.

For my share of suggestion -
试译:
武术和功夫原是一家，息息相关。
Marshal art and kung fu have a cognate and symbiotic relationship.