. . . is one of those completely obvious things that we just ignore for the most part. But what you can say about some part of the world--any part--is that, given the part is finite in extent, over some interval of time there will be changes that can be recorded. And you can say there is an initial state and a final state, ignoring all the information about changes in between. In fact, recording all the information is equivalent to having a copy of everything that can be known about changes in state, of everything in this part. We might be able to record information over extremely short intervals, but the cost of doing this in some kind of iterated way is too much, and there's the rub. So the problem seems to amount to not having enough time to record everything, so lots of information is discarded, over . . . time. The physics of measurement imply that there is no classical device that can "record everything" Naive question #1: what happens to this not-recorded information?
Depends if it is transient ie this morning did I put my lady sock on first or second? If not recorded in some manner, put into a savable physical format, it will not only never be known it will never be known it was a detail which could have been known had it been recorded If it is fundermental information, gravity, it remains in existence awaiting discovery Please Register or Log in to view the hidden image!
Well, the information may not be preserved, but the thing from which the information is being received still exists, until the thing essentially disintegrates. I can record a lot of information about an apple, but the only exhaustive source of information is the apple itself. And it will eventually disassemble. The apple never goes away. Although they will be transformed into components, the properties of the apple are preserved: its atoms, its mass, its chemical energy, its kinetic and potential energy, its heat - even its gravitational effect on celestial bodies. One apple's worth of all these properties remain in the system - if you define the system sufficiently broadly.
Another obvious point, almost an axiom. But careful about information being 'preserved'. What I mean is there's a copy, because some device 'registered' a change in something and the information is stored in a memory. Although in physics, information would include the physical thing you record the copy of, or part of. Like an apple. That follows because information about changes over time, in the apple, isn't an apple but both are necessarily physical.
The apple will be transformed into dung or compost. The apple is just one of many possible forms using earth elements. If compost, its elements may reappear as a carrot, depending on whose garden. Life cycles include production and recycling. In this sense, everything is temporary.