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a(t) = e^(HT)

Where the distance between any two objects are

D(t) = a(t)Δx

Where x does not measure physical distance, but a conventional coordinate distance.

This means that eventually any physical distance (Even quantum wavelengths) will grow exponentially and eventually a big rip will happen. My question is how can the universe truly reach heat death or thermal equilibrium if its going to expand so fast in the far future? My intuition tells me that it will asymptotically approach maximum entropy.