The Canonical Distribution and Stochastic Differential Equations

  • Ben Leimkuhler
  • Charles Matthews
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 39)


Until now, we have considered molecular models for isolated collections of atoms. We have seen how to derive equations of motion, and studied the properties of the relevant dynamical systems. We have also observed that the chaotic nature of a typical system imparts a random aspect which suggests that the dynamics defines, at least in some approximate sense, a limiting probability distribution.


Random Walk Stochastic Differential Equation Wiener Process Canonical Ensemble Heat Bath 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ben Leimkuhler
    • 1
  • Charles Matthews
    • 2
  1. 1.School of MathematicsUniversity of EdinburghEdinburghUK
  2. 2.Gordon Center for Integrative ScienceUniversity of ChicagoChicagoUSA

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