It is also the case that for a given mean A and standard deviation S the Gaussian probability distribution for random noise is itself a maximum entropy solution. Any other probability distribution has worse entropy. For a simple proof see (or DIY it with calculus of variations).
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Other noise probability distributions would just make things worse.
The long and the short of it is that Shannon is about as unassailable on the fundamentals of information theory as Einstein is on relativity.
Sadly this does not stop cranks from regularly popping up.