Brussels-Austin Nonequilibrium Statistical Mechanics in the Later Years: Large Poincare Systems and Rigged Hilbert Space

Abstract

This second part of a two-part essay discusses recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their similarity transformation approach (see Part I), but the contemporary approach utilizes rigged Hilbert space (whereas the older approach used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, the use of similarity transformations shifts to the background. In its place arose an interest in the physical features of large Poincar\U{e9} systems, nonlinear dynamics and the mathematical tools necessary to analyze them.