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gjm comments on Entropy and Temperature - Less Wrong
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Temperature in the thermodynamic sense (which is the same as the information-theoretic sense if you have only ordinary macroscopic information) is the same as average energy per molecule, which has a lot to do with phase changes for the obvious reason.
In exotic cases where the information-theoretic and thermodynamic temperatures diverge, thermodynamic temperature still tells you about phase changes but information-theoretic temperature doesn't. (The thermodynamic temperature is still useful in these cases; I hope no one is claiming otherwise.)
You probably know this, but average energy per molecule is not temperature at low temperatures. Quantum kicks in and that definition fails. dS/dE never lets you down.
Whoops! Thanks for the correction.
Aha, thanks. Is information-theoretic temperature observer-specific?
In the sense I have in mind, yes.
I am somewhat amused that you linked to the same post on which we are currently commenting. Was that intentional?
Actually, no! There have been kinda-parallel discussions of entropy, information, probability, etc., here and in the Open Thread, and I hadn't been paying much attention to which one this was.
Anyway, same post or no, it's as good a place as any to point someone to for a clarification of what notion of temperature I had in mind.