Dynamics of Open Classical Systems

  • Ángel S. Sanz
  • Salvador Miret-Artés
Part of the Lecture Notes in Physics book series (LNP, volume 850)


The theoretical framework for dissipative and stochastic dynamics of open classical systems is presented and discussed. Only linear friction is explicitly considered. In spite of the different approaches one may find in the literature, there are essentially three main ways to introduce stochasticity. First, phenomenologically, describing Brownian-like motions by means of the standard Langevin equation, where the system-environment interaction is governed by two parameters: temperature and friction. Second, by starting from the Liouville equation, which is satisfied by any dynamical variable. And third, the system-plus-bath approach, where the equations of motion can be expressed in terms of a generalized Langevin equation. System trajectories issued from solving such equations describe erratic or random motion and, therefore, they are usually called (classical) stochastic trajectories. In those cases where noise becomes negligible or zero, the stochastic dynamics becomes dissipative (trajectories then become smoother).


Brownian Motion Harmonic Oscillator Configuration Space Langevin Equation Planck Equation 
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-Verlag Berlin Heidelberg  2012

Authors and Affiliations

  • Ángel S. Sanz
    • 1
  • Salvador Miret-Artés
    • 1
  1. 1.Instituto de Física FundamentalConsejo Superior de Investigaciones CientíficasMadridSpain

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