The person who coined the expression "The only constant is change" was the Greek philosopher Heraclitus in roughly the fifth century BCE, so he wasn't really thinking about entropy when he said that. He was thinking about the fact that reality is always in a state of flux. Nothing remains the same forever. He famously claimed that a person could not technically step in the same river twice. The theory of thermodynamics didn't come about until the 19th century CE.
The theory perhaps; but early understandings of it, vague and fuzzy, pervaded. An early understanding of it is as such, "the only constant is change". Thermodynamics didn't just start being a reality when someone pinned it down so it couldn't keep squirming; it was always there and making certain things true.
I don't think he could have made the observation if not for the truth of such things as the demands of entropy and information theory that demand change.
Of course I'm also aware at this point that I'm a little wrong about which fundamental property of the universe resolves to "things gotta change, and every moment is unique in microstate."
Still, the fact is that different things can still have the same image on them, and certain things translate between image and instantiation.