Entropy, Information and Quantum Geometry
This Chinese apophthegm paraphrases here the equivalent one “Entropy is not Shannon Entropy”. There are in fact at least two things wrong with Shannon entropy. The first is its name: had Claude Shannon not accepted John von Neumann’s advice (“you should call it entropy and for two reasons: first, the function is already in use in thermodynamics under that name; second and more importantly, most people don’t know what entropy really is, and if you use the word “entropy in an argument, you will win every time (1)”) and just called it “uncertainty”, endless confusion would have been spared. “Entropy” is psychologically tied with “thermodynamics” in a physicist’s mind, so that the purely logical, far wider connotation of Shannon’s concept escapes attention. Shannon entropy is simply and avowedly the “measure of the uncertainty inherent in a preassigned probability scheme”; as such it has nothing whatever to do with thermodynamica1 entropy, except in the case in which that probability distribution is known, or proven to be, “canonical”.
KeywordsShannon Entropy Cross Entropy Quantum Geometry White Horse Abelian Gauge Field
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