Dear All, I thought the list members may be interested in the following recent note of Misha Gromov which *very* carefully uses ideas of category theory to talk about entropy. Particuarly, his point of view on category theory may be appealing. In a Search for a Structure, Part 1: On Entropy. June 19, 2012 http://www.ihes.fr/~gromov/PDF/structres-entropy-june-2012.pdf At the end of the paper, he says: Yet, I hope that I managed to convey the message: the mathematical language d eveloped by the end of the 20th century by far exceeds in its expressive power anything, even imaginable, say, before 1960. Any *meaningful* idea coming from science can be fully developed in this language. In the paper, he also says: To see this, you just need to realize that ”something” of a physicist, is a covariant functor from a suitable ”category of protocols” to the category of sets – outcomes of exper- iments; all you have to do afterwards is to follow the guidelines prescribed by the syntax of category theory. (Arguably, the category language, some call it ”abstract”, reflects mental undercurrents that surface as our ”intuitive reasoning”; a comprehensive math- ematical description of this ”reasoning”, will be, probably, even farther removed from the ”real world” than categories and functors.) Sincerely, Misha [For admin and other information see: http://www.mta.ca/~cat-dist/ ]