Phase Space Distributions and Microcanonical Averages

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


In the previous chapters, we considered the approximation of Hamiltonian trajectories. In this chapter we study the paths emanating from the collection of all initial conditions within a given set. This is the starting point for statistical mechanics which allows the calculation of averages.


Phase Space Invariant Measure Liouville Equation Solution Operator Invariant Distribution 
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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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