Comment by A_D_E_P_T

> "In the introduction, we stated that, since a CTC is a compact set, there is an event x0 where the entropy of the spaceship is minimal. In the proximity of such event, our macroscopic notion of causation breaks down. This is evident in figures 2 and 3, where the existence of the low-entropy state at proper time T does not have any macroscopic cause in its near past or future. It just 'fluctuates into existence'. Indeed, any form of order that the event x0 carries (including objects and people) has no logical cause that can be expressed in purely macroscopic terms. For example, if there is a book, nobody wrote it. If a person has a memory, this memory is illusory, and its content is meaningless (by human standards). This is because our notions of 'writing' and 'forming a memory' implicitly rely on increasing entropy [1], and there is no event with lower entropy than x0."

I don't believe that "our notions of 'writing' and 'forming a memory' implicitly rely on increasing entropy." Entropy's relation to the arrow of time is complex but it's enough for entropy to be non-static, and for things to durably exist in the world, for there to be a notion of movement in time. If something was written at time T, entropy fluctuated into a minimum at T+100, and entropy increased again at T+200, at all points the original writing event would be traceable back to T.

Time appears to stop and things become causally disconnected from each other when entropy reaches minima or maxima and stays there. Even so, local fluctuations can lead to the emergence of an arrow of time -- e.g. if a glucose molecule coalesces out of the void, you can measure time by it, as it's not perfectly stable.