There is a good article in the New Scientist this weekend by Mark Buchanan about Constantino Tsallis and his work on non-extensive statistical mechanics and q-entropy. Buchanan, I think, does a great job of laying out the debate on q-entropy, fairly addressing both sides. For those not in the know, q-entropy is an attempt to generalize Boltzmann-Gibbs statistical mechanics so that it can describe systems other than those which exhibit thermal equilibriums. Think chaotic systems where things like turbulence prevent the system from ever settling down. While there are a number of physicists who think this work is bunk, with criticisms ranging from complaining that the equations are unnatural to complaining that it's nothing more than fitting power laws to complaining that the equations have led to no new predictions, there are also literally thousands of physicists from all over the world who think this work is deeply significant not only for its theoretical interest but also because it gives them an arsenal of tools they can use to characterize phenomena that exhibit some degree of chaos that are outside the scope of traditional statistical mechanics. Since Tsallis first published his ideas, thousands of papers have been written on the subject and the community of physicists working in the area of non-extensive statistical mechanics has been growing leaps and bounds. This, of course, has those firmly based in the establishment up in arms since they can't help but pick up a copy of any of the top physics journals and not see some article on the subject. Having read Tsallis' draft letter to the editor of the New Scientist this weekend wherein he addresses the concerns of his critics, I am obviously favorable to his research programme even if I don't fully understand all the intricate mathematical minuatie. What is clear to me is that most of the critics haven't done their homework and simply have not read enough of the theoretical contributions to understand how rigorous much of the work is and also are not familiar with many of the predictions that have been made and then later empirically substantiated. There are still holes in the research programme, as Tsallis will be the first to admit, but the research programme is still early on and when looked at in the context of how long it took for traditional statistical mechanics to reach a level of maturity where most of the holes were kinked out, one shouldn't be too harsh.
Update: The New Scientist published Tsallis' response but chopped off about 90% of it. Some of the strongest arguments were excluded.
