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, pages1268-9.

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(1-q)-1)/(1-q) 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

American Mathematical Society