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I wish I knew what exactly "information" is in this context. I know a couple of definitions, but none seems to match.
What is needed, I believe, is a definition of information that is as rigorous as, say, the definition of energy. By the way, a fundamental tenet of Shannon's theory is that (quantity of) information is defined in terms of the _expectation_ of its recipient, so it seems a rather different beast than the quantities with which physics deals.