Brussels-Austin nonequilibrium statistical mechanics in the later years: Large poincaré 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 Poincaré systems, nonlinear dynamics and the mathematical tools necessary to analyze them.

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Robert Bishop
Wheaton College, Illinois

Citations of this work

Arrow of Time in Rigged Hilbert Space Quantum Mechanics.Robert C. Bishop - 2004 - International Journal of Theoretical Physics 43 (7):1675–1687.

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References found in this work

The end of certainty: time, chaos, and the new laws of nature.I. Prigogine - 1997 - New York: Free Press. Edited by Isabelle Stengers.
Arrow of Time in Rigged Hilbert Space Quantum Mechanics.Robert C. Bishop - 2004 - International Journal of Theoretical Physics 43 (7):1675–1687.
Quantum time arrows, semigroups and time-reversal in scattering.Robert C. Bishop - 2005 - International Journal of Theoretical Physics:723-733.

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