By reasoning, and through use of quantum statistical mechanics, Gavassino shows the time tourist's own entropy can't continue to grow as they 'go back', with quantum fuzziness effectively canceling expected disorder to create a parallel entropic timeline that begins and ends at the same points.

Entropic arrow of time (gray arrows) flipping between entry and exit points of a closed timelike circuit. (Gavassino, Classical and Quantum Gravity, 2024)

What would that look like for the contents of the temporally looped spaceship? Processes that we might expect to be linked to entropy would necessarily change, potentially reversing.

Circling back to a spry young grandfather courting your grandmother the first time, the time loop could make his untimely death reversible; your memory of why you ever wanted to murder him in the first place may be erasable. In other words, all bets are off in a closed loop where quantum physics smoothes out any intrusive entropy