I think the issue is that the arrow of time, the perceived direction of time, IS the increasing of entropy. We observe changes in state, seemingly always in the direction of increased disorder of the system, and we refer to this experience as "the arrow of time". I think time, fundamentally, is very much the twin of space in the multiverse as a whole, where any potential agent could traverse it in a non-linear fashion, but once a universe is closed off, time loses this quality(as it is cut off from meta-time, if I can call it that) and what we experience as time is only the system changing state from ordered to disordered to final total dispersion of matter/energy. As the article stated, no matter what way the arrow "points" it's just always going from ordered state to disordered, so the terms, imo, are really synonymous or a tautology, an arrow of time IS the overall increasing of disorder, as perceived by a conscious agent(us). I don't see it as circular because we experience a flow of time and observe this "flow" only in terms of change and only in the direction of increased entropy, forming our arrow of time, which is just a description of particularly difficult concept to articulate. Personally, I think this hypothesis is the most compelling of the multi-versal ideas of time. Sorry if I misunderstood you and totally missed your point, but that's my take on it. =)

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