Related papers: Robert W. Zwanzig: Formulated nonequilibrium stati…
We give a pedagogical introduction to a selection of recently discussed topics in nonequilibrium statistical mechanics, concentrating mostly on formal structures and on general principles. Part I contains an overview of the formalism of…
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
A two-temperature linear spin model is presented that allows an easily understandable introduction to non-equilibrium statistical physics. The model is one that includes the concepts that are typical of more realistic non-equilibrium models…
This is a biographical sketch and tribute to Abraham Robinson (1918-1974) on the 95th anniversary of his birth with a short discussion of the place of nonstandard analysis in the present-day mathematics.
The article is dedicated to recalling the life and mathematics of Louis Nirenberg, a distinguished Canadian mathematician who recently died in New York, where he lived. An emblematic figure of Analysis and Partial Differential Equations in…
This paper is an introduction to the von Neumann entropy in a historic approach. Von Neumann's gedanken experiment is repeated, which led him to the formula of thermodynamic entropy of a statistical operator. In the analysis of his ideas we…
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical…
Jonathan M. Borwein (1951-2016) was a prolific mathematician whose career spanned several countries (UK, Canada, USA, Australia) and whose many interests included analysis, optimisation, number theory, special functions, experimental…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
An analogy is developed between the breaking of space-inversion symmetry in equilibrium statistical mechanics and the breaking of time-reversal symmetry in nonequilibrium statistical mechanics. In this way, similar relationships…
A collection of brilliant and original unfinished ideas by Wladyslaw Marcinek (1952-2003) in particle interactions, categorical approach to generalized statistics, qubits and quantum logic, entwined operators, cobordisms and noncommutative…
Hans Grauert died in September of 2011. This article reviews his life in mathematics and recalls some detail his major accomplishments.
Classical statistical mechanics of macroscopic systems in equilibrium is based on Boltzmann's principle. Tsallis has proposed a generalization of Boltzmann-Gibbs statistics. Its relation to dynamics and nonextensivity of statistical systems…
With this note, we remember our friend Maria Krawczyk, who passed away this year, on May 24th. We briefly outline some of her physics interests and main accomplishments, and her great human and moral qualities.
Some reflections on the role in the development of Mathematics of our unconscious perception of the world and just as unconscious organizing pulsions for those perceptions.
Professor Richard H. Dalitz passed away on January 13, 2006. He was almost 81 years old and his outstanding contributions are intimately connected to some of the major breakthroughs of the 20th century in particle and nuclear physics. These…
The prominent Russian mathematician Igor Rostislavovich Shafarevich passed away on February 19, 2017. In this article we supply his biography, discuss his many important contributions to number theory, algebra and algebraic geometry, and…
A brief review on the dynamical systems approach to nonequilibrium statistical mechanics and chaotic dynamics
A survey of the approach to Statistical Mechanics following Boltzmann's theory of ensembles and ergodic hypothesis leading to chaoticity as a unifying principle of equilibrium and nonequilibrium Statistical Mechanics.
The present review is based on the lectures that the author had been giving during several years at the Swiss Federal Institute of Technology in Zurich (ETH Zurich). Being bounded by lecture frames, the selection of the material, by…