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Lyapunov Instabilities of Extended Systems

  • Hong-liu Yang
  • Günter Radons
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 52)

Abstract

One of the most successful theories in modern science is statistical mechanics, which allows us to understand the macroscopic (thermodynamic) properties of matter from a statistical analysis of the microscopic (mechanical) behavior of the constituent particles. In spite of this, using certain probabilistic assumptions such as Boltzmann’s Stosszahlansatz causes the lack of a firm foundation of this theory, especially for non-equilibrium statistical mechanics. Fortunately, the concept of chaotic dynamics developed in the 20th century [1] is a good candidate for accounting for these difficulties. Instead of the probabilistic assumptions, the dynamical instability of trajectories can make available the necessary fast loss of time correlations, ergodicity, mixing and other dynamical randomness [2]. It is generally expected that dynamical instability is at the basis of macroscopic transport phenomena and that one can find certain connections between them. Some beautiful theories in this direction were already developed in the past decade. Examples are the escape-rate formalism by Gaspard and Nicolis [3, 4] and the Gaussian thermostat method by Nosé, Hoover, Evans, Morriss and others [5, 6], where the Lyapunov exponents were related to certain transport coefficients.

Keywords

Lyapunov Exponent Extend System Lyapunov Spectrum Coordinate Part Momentum Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  • Hong-liu Yang
    • 1
  • Günter Radons
    • 1
  1. 1.Institut für PhysikTechnische Universität ChemnitzChemnitzGermany

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