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indefinitely not due to the growth channel output entropy (which, on the contrary, decreases), but due

to the fact that the noise entropy (the subtrahend in (19)) tends to minus infinity:
lim H ( ) ξ = −∞ . (21)
N→ 0
This observation contradicts the physical meaning which is inherent in the definition of the
difference (14). This change in the sign and adding of the subtrahend to the output entropy occurs

already at "weak" noise: N ≤ (2eπ ) − 1 . It is difficult to understand the physical meaning of this

phenomenon. Although in the form (20) the capacity formula shows the monotonicity of the function
( )
CN at N → 0 , that allows to explain this phenomenon by the difference between determining

differential and discrete entropy, noted earlier. However, due to the lack of a clear physical
interpretation of this phenomenon, correctness of the analytical derivation of capacity by using the

concepts of the differential entropy and the average mutual information is doubtful.
As we will see later, attributing to this formula the ability to determine the upper limit of data

transmission rates for the Gaussian channel is even more doubtful.

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