Microscopic Chaos, Fractals and Transport in Nonequilibrium Statistical Mechanics

cft book coverby Rainer Klages (Queen Mary, University of London, UK)
Advanced Series in Nonlinear Dynamics Vol. 24, World Scientific, Singapore, June 2007; 456 pages; ISBN 978-981-256-507-5

A valuable introduction for newcomers as well as an important reference and source of inspiration for established researchers, this book provides an up-to-date summary of central topics in the field of nonequilibrium statistical mechanics and dynamical systems theory.

Understanding macroscopic properties of matter starting from microscopic chaos in the equations of motion of single atoms or molecules is a key problem in nonequilibrium statistical mechanics. Of particular interest both for theory and applications are transport processes such as diffusion, reaction, conduction and viscosity.

Recent advances towards a deterministic theory of nonequilibrium statistical physics are summarized: Both Hamiltonian dynamical systems under nonequilibrium boundary conditions and non-Hamiltonian modelings of nonequilibrium steady states by using thermal reservoirs are considered. The surprising new results include transport coefficients that are fractal functions of control parameters, fundamental relations between transport coefficients and chaos quantities, and an understanding of nonequilibrium entropy production in terms of fractal measures and attractors.

The theory is particularly useful for the description of many-particle systems with properties in-between conventional thermodynamics and nonlinear science, as they are frequently encountered on nanoscales.

Contents:
  • Deterministic Diffusion
  • Deterministic Drift-Diffusion
  • Deterministic Reaction-Diffusion
  • Deterministic Diffusion and Random Perturbations
  • From Normal to Anomalous Diffusion
  • From Diffusive Maps to Hamiltonian Particle Billiards
  • Designing Billiards with Irregular Transport Coefficients
  • Deterministic Diffusion of Granular Particles
  • Motivation: Coupling a System to a Thermal Reservoir
  • The Gaussian Thermostat
  • The Nosť-Hoover Thermostat
  • Universalities in Gaussian and Nosť-Hoover Dynamics?
  • Gaussian and Nosť-Hoover Thermostats Revisited
  • Stochastic and Deterministic Boundary Thermostats
  • Active Brownian Particles and Nosť-Hoover Dynamics
  • Further Topics in Chaotic Transport Theory
Readership: Graduate students and researchers interested in statistical physics and nonlinear dynamics of nonequilibrium systems.
  • reviews and related material:
    • was listed under Bestsellers in Nonlinear Science of the publisher in Fall 2007 and again in Spring 2008
    • reviews:
      • Amazon.com: ``This book gives an excellent, balanced and up to date review of the subject matter. Highly recommended for students of nonequilibrium statistical mechanics.'' (D.J.Evans, Canberra)
      • Zentralblatt Mathematik: ``An author interested in these questions will find there many suggestions for further research.'' (G.Jumarie, Montreal)
      • Contemporary Physics: ``Important and key concepts in dynamical systems theory or nonlinear dynamics [...] have played an important role in the recent studies in nonequilibrium statistical mechanics. This book precisely shows some of the key contributions to the field. [...]  The bibliography
        provided in the monograph is very extensive and comprises most of the literature on the field.  [...]  The book would be of interest for graduate students and researchers interested in recent progress in the field and those attempting to enter it. Physicists interested in the applications of chaos theory into statistical mechanics can also benefit from its reading.'' (M.A.F.Sanjuan, Madrid)
  • updated list of references: Please note that references cited in the book were originally collected until Fall 2006. Further literature that appeared afterwards and is relevant for the topics covered by the book you can find here.
  • corrections: if you spot a mistake, please let me know! A current list you can find here.
  • comments are most welcome - please feel free to contact me
  • this book online:
    • on Amazon.com, where you can electronically search inside the whole book; see also there for a first rating of the book
    • on Google Books, where you can read through many taster chapters
last update: 06/06/2011