Mathematical Digest
Short Summaries of Articles about Mathematics in the Popular Press"A Fresh Take on Disorder, or Disorderly Science?", by Adrian Cho. Science, 23 August 2002, pages12689. The title refers to a new definition of entropy, its proponents and opponents.The definition formulated by Ludwig Boltzmann, and accepted for almost acentury, is that entropy is k(ln W), where k is constant andW is the number of "equivalent microscopic arrangements" of a system.Constantinos Tsallis of the Brazilian Center for Research in Physics hasproposed that entropy be defined as k(W^{(1q)}1)/(1q) whereq is a parameter (whose definition isn't entirely clear). A quickapplication of L'Hôpital's Rule shows that as q approaches 1, thelimit of the proposed expression for entropy equals the standard expression.Tsallis says that the old formula for entropy applies when a system is inequilibrium, but his formula becomes relevant when a system is far fromequilibrium. The article presents viewpoints from both sides as to thedesirability of adopting Tsallis' formula.  Mike Breen
