I'm not really sure why you say volume is changing here.
I don't understand how you want information to be used, if not to calculate a final distribution over microstates, or what you think "losing information" is if not an increase in entropy. If we're having some sort of disconnect I'd be happy to talk more, but if you're trolling me I would like to not be trolled.
I'm not really sure why you say volume is changing here.
Think about putting a packet of gas next to a vacuum and allowing it to expand. In this case it's even easier to see that the requirements of your thought experiment hold - you know the exact state of the vacuum, because it has no microstates. Yet the total system entropy will still increase as the molecules of gas expand to fill the vacuum. Even if you have perfect information about the gas at the beginning (zero entropy), at the end of the experiment you will not. You will have some uncertainty. ...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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