Presentation by Joel L. Lebowitz,
Chairman, IUPAP C3 Commission on Thermodynamics and Statistical Physics

Dvid Ruelle and Yasha G. Sinai: Boltzmann Medallist 1983

The award of Boltzmann Medal to David Ruell and Yasha G. Sinai recognizes their contributions to statistical mechanics: contributions both fundamenal and oractical, the have given us not only many new exact reslut, but also novel ways of thinking about statistical mechanics, thus revealing its breadth and great inner beauty.

I still find it amazing that the foundations laid by Boltzmann, Gibbs, Einstein, and others have held firm as statistical meachnics has extended to become an essential ingredient of all science, from pure mathematics to applied biology. the works of Ruelle and Sinai have certainly contributed greatly to both crown and the root of our beautiful subject.

I cannot and will not try to enumerate all important theorems proven by david Ruelle and Yasha Sinai. You can find one aspect of their work described in their joint article in this volume. This relates a very deep level the time invariant measure of certain dynamical system to Gibbs measures of partocles on one dimensional lattice (with translation playing the role of time shifts). these beautiful results (which are truly joint ones despite the fact that this is their first joint paper) have their origin in the incisive characterization of Gibbs states provided by the Dobrushin-Lanford-Ruelle equations and (good) dynamical systems by Kolmogorov-Sinai entropy. The lecture was given by Ruelle sinice by mentioning briefly a few other topics to which our boltzmann medalists have made deep contributions.

Rullel and Taken's paper, showing that th onest of trbulence can ocur directly as a transition from quasi-periodic motion with as few as three frequencies, opened the way for a new era in the theoretical and experimental study of this subject. the problem of fully sign post on the way Ruelle's upper nound on the density of positive Lyapunov exponents.