Heapsort, Quicksort, and Entropy

Numerous web-pages compare heapsort and quicksort. Most of them say something along the lines of `both take an average time scaling as N log N, but A good implementation of QUICKSORT usually beats HEAPSORT in practice.' Some take this folklore a bit further, giving quantitative details: `On average the number of comparisons done in HEAPSORT is about twice as much as in QUICKSORT, but HEAPSORT avoi

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see also TAOCP vol3 pp148 section 5.2.3, pp156 question 18, pp181 section 5.3.1.