this post was submitted on 21 Apr 2024
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I think there is in fact a notion of continuous entropy where that is actually true, and it does appear to be used in statistical mechanics (but I am not a physicist). But there are clearly a lot of technical details which have been scrubbed away by the LW treatment.
The fact that the naive continuous version of the Shannon entropy (just replacing the sum with an integral) can go negative is one reason why statistical physicists will tell you not to do that. Or, more precisely: That's a trick which only works when patched up by an idea imported from quantum mechanics.
yea i did try to read the lecture notes and got reminded very fast why i don't try to read physics writing lol