From Trajectories to Ensembles in Classical Mechanics

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


The time-evolution of interacting “small” systems is usually described by means of quantum mechanics. However, very often, it happens that a first approach to these dynamics by means of classical mechanics provides a better understanding of the processes and phenomena involved. Here, an overview on classical mechanics is presented, ranging from regular motions to chaos which induces intrinsic stochasticity. This allows to establish a direct link to classical statistical mechanics within the Liouvillian framework when dealing with particle ensembles, where motion is still deterministic but unpredictable. On these grounds, some criteria to discern whether a system has to be considered as classical or quantum mechanical will be analyzed. Finally, different aspects of the continuum limit of classical mechanics of many bodies will also be presented in order to better contextualize later on in this Volume the quantum and optical hydrodynamical interpretations.


Phase Space Periodic Orbit Hamiltonian System Classical Mechanic Chaotic Dynamic 
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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