19 - What's next?

Summary

We have now covered the background material needed to approach the literature on dynamical systems theory and nonequilibrium statistical mechanics. Here we list a few topics that you might find stimulating to think about. Some references are provided, but you should spend some time on the computer looking up relevant papers in areas that you find especially interesting.

Very nice overviews of this field of research are provided by D. Ruelle and Ya. G. Sinai in their paper ‘Prom dynamical systems to statistical mechanics and back’ [RS86]; in Ruelle's lecture notes, ‘New theoretical results in nonequilibrium statistical mechanics‘ [Rue98]; and in the paper of G. Gallavotti, ‘Chaotic dynamics, fluctuations, nonequilibrium ensembles’ [Gal98].

A very beautiful and more advanced discussion of many of the topics covered in the later chapters of this book is provided in the monograph Chaos, Scattering, and Statistical Mechanics [Gas98], by P. Gaspard. Some general reviews of these subjects can also be found in papers by Gaspard; van Beijeren and Dorfman; Cohen; Dellago and Posch; Morriss, Dettmann and Rondoni, in Physica A, 240 Nos. 1–2 (1997), and in the Chaos Focus Issue: Chaos and Irreversibility [TGN98].

Billiard systems

In this book, we have only touched lightly the deep and rich subject of the dynamical theory of hard-sphere systems. This area has been developed by Sinai and co-workers and constitutes one of the most fascinating areas for study – it is a field of beautiful mathematics and of major physical interest.