A simple example where information-theoretic entropy is used where there is no physical representation: Video codecs.
I'm guessing you've heard of mpeg and h.264 encoding. Which one encodes a movie better? One way of answering this question is to ask: Which codec added less entropy (perhaps for the same compression)?
For that matter: Before Shannon's information entropy, one might wonder if there is a way (another codec) perhaps recovering the information after mpeg coding and decoding. However, now you know that information-entropy can only increase or stay the same, which tells you that subsequent "correction codec" cannot remove entropy introduced by mpeg codec.
Thanks. I don't really like that example with codecs, because I could always argue that any codec can only be a physical system, operating in some environment at temperature T and will be constrained by Landauer's, ets.
Either way, I think we've digressed. I'm actually very happy with yours: "Adding energy to a system with negative temperature reduces the number of microstates.", because this is clear and unambiguous.
I'm guessing you've heard of mpeg and h.264 encoding. Which one encodes a movie better? One way of answering this question is to ask: Which codec added less entropy (perhaps for the same compression)?
For that matter: Before Shannon's information entropy, one might wonder if there is a way (another codec) perhaps recovering the information after mpeg coding and decoding. However, now you know that information-entropy can only increase or stay the same, which tells you that subsequent "correction codec" cannot remove entropy introduced by mpeg codec.