The Gibbs neg-entropy -ηG=∫ II ln II is compared to the Shannon negentropy ηs=∑p Inp. The coarse-grained density is II, whilep is a probability sequence. Both objects are defined over partitions of the energy shell within a set-theoretic framework. The dissimilarity of these functionals is exhibited throughηG vs.GηS curves. A positive information interpretation of ηG is given referring it to the maximum information contained in the solution to the Liouville equation. The physical relevance ofηG over ηS in classical physics is argued. In quantum mechanics, the fine-grained Shannon entropy remains relevant to the uncertainty principle, while the coarsegrained densities maintain their properties as in the classical case.