Let's say I am in a gym and had an eye contact with a person working out next to me, is it OK to say
What are the best simple expression to break the ice with complete strangers?
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Both of these sound a pretty unnatural and even in English I can't think of many times where I would just say "how are you" to break the ice to someone working at the gym next to me. Something just like
こんにちは is good because they will most likely reply back, and you can use that as a bouncing point. After that you can say something like
スニーカー、かっこいいね (Your shoes are pretty cool) or some other "in." If they don't reply back and just nod, it's most likely a no-go (depending on the situation) but other things you could say to start something are:
ああ、疲れた~ - Saying this out loud after eye contact or
こんにちは might prompt a response like
お疲れ様です and maybe can lead into a conversation
すみません、今何時ですか might work if you can lead into some kind of conversation after asking the time.
Just a word to the wise, but you should probably figure out if the eye contact is a "I'm interested in chit-chat" and not a "Oh a non-japanese person is in the gym"