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please reword the title of this question to something that sums up the body in one complete sentence. It should be a clear descriptor, not a generic heading.
You seem to contradict yourself. On one hand, CPT symmetry indicates that time flowing forwards and time flowing backwards are just two sides of the same coin, but then on the other hand you say entropy grows with time. In the time-flowing-backwards scenario, wouldn't entropy decrease? That does seem to make a distinction between "past" and "future."