2003/04/07 by Robert C. Bishop, Bishop, Robert C. · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical Physics (physics.class-ph) #Classical mechanics #FOS: Physical sciences #General Physics (physics.gen-ph) #Hilbert space #Mathematical physics #Non-equilibrium thermodynamics #Philosophy #Physics #Poincaré conjecture #Quantum mechanics #Reproducing kernel Hilbert space #Rigged Hilbert space #Space (punctuation) #Statistical Mechanics and Entropy #Statistical mechanics #Statistical physics #Theoretical and Computational Physics #Theoretical physics #physics.class-ph #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0304020
published in arXiv (Cornell University) (Cornell University) · 23 pages, Part II of two parts; updated institutional affiliation
openalex publication_date 2003/04/07 · arxiv created 2003/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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\Ue9 systems, nonlinear dynamics and the mathematical tools necessary to analyze them.