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Of course, my understanding of the problem is only preliminary. But the generality requirement seems artificial: surely a memory that records the only future configuration of the system remembers the future in a deterministic world, there being no "what ifs" regarding that state? Why couldn't it occasionally be a memory of the future for that matter? Explanation (2) leaves no such ambiguity. So what? It doesn't have anything to say on the nature of that memory. Yes, increase of (new) memory happens only as total entropy of the universe increases. My problem with explanation (1) is that even if it's correct, it doesn't seem to be a complete answer in itself. This fine-tuning disqualifies it as a bona fide memory. So any memory of the future of the system "could remember only one possible configuration of that system".

But the smallest changes in the future state destroy the thermodynamic arrow of time between now and the future. Specifically, they argue that a memory should be somehow robust to small microscopic changes in states of the system it records (what they call "generality" requirement). The conclusion is arrived by imposing some constraints on what a memory system should be like.

More recently, People have argued that even reversible and non-dissipative memory systems are subject to PAOT (Mlodinow and Brun, 2014).

to cause our neurons to orient in a particular fashion, requires energy which results in our body heating up a little bit, increasing the total entropy (Hawking, 19) The initialization of memory to make it reusable is an irreversible process that increases total entropy (Landauer, 1961.

Practical memory systems work in a way that the formation of new memories entails an overall increase of total entropy of the system and the environment.

If so (maybe not?), how do the two relate? So it is generally thought that PAOT is a consequence of the thermodynamic arrow of time of our universe. Here the past is understood as a moment or time when the entropy of the universe was lower, and contrarily for the future. The question is sometimes referred to as the "psychological arrow of time" (Hawking, 1985). Eric Asks: Why do we remember the past but not the future?