Gibbs’ entropy is derived from “the probability that an unspecified system of the ensemble (i.e. one of which we only know that it belongs to the ensemble) will lie within the given limits” in phase space. That’s the “coefficient of probability” of the phase, its logarithm is the “index of probability” of the phase, the average of that is the entropy.
Of course the probability distribution corresponds to the uncertainty. That’s why the entropy is defined from the probability distribution.
Your claim sounds like saying that the area of a polygon cannot be a measure of its extension because the extension is given by the shape and calculating the area doesn’t tell us anything new.
Gibbs’ entropy is derived from “the probability that an unspecified system of the ensemble (i.e. one of which we only know that it belongs to the ensemble) will lie within the given limits” in phase space. That’s the “coefficient of probability” of the phase, its logarithm is the “index of probability” of the phase, the average of that is the entropy.
Of course the probability distribution corresponds to the uncertainty. That’s why the entropy is defined from the probability distribution.
Your claim sounds like saying that the area of a polygon cannot be a measure of its extension because the extension is given by the shape and calculating the area doesn’t tell us anything new.