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Entropy

Properties

• The entropy of a discrete distribution over \(N\) elements is bounded by \(\log N\)

Proof: Use Gibb’s Inequality, setting \(q_n = 1/N\). Then \(H(p) \leq -\sum_n p_n \log \frac{1}{N} = \log N (\sum_n p_n) = \log N\)