Journal of Elasticity

, Volume 100, Issue 1–2, pp 5–24 | Cite as

Translation of Walter Noll’s “Derivation of the Fundamental Equations of Continuum Thermodynamics from Statistical Mechanics”

  • Richard B. LehoucqEmail author
  • Anatole Von Lilienfeld-Toal


This article represents a translation of the original paper, “Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der Statistischen Mechanik”, which was written by Walter Noll and appeared in the Journal of Rational Mechanics and Analysis 4 (1955), 627–646. In the original paper, Noll addressed and analyzed the seminal paper of Irving & Kirkwood, published five years earlier, on “The statistical mechanical theory of transport processes. IV, The Equations of Hydrodynamics.” Noll gave new interpretations and provided a firm setting for ideas advanced by Irving & Kirkwood that clearly and directly related to the basic principles of continuum mechanics. This translation aims to expose the important contribution of Noll to a wider community of researchers at a time when the atomistic modeling of material behavior is being advanced. Noll’s use of elementary mathematics to discover physical effects, to explain physical concepts, and to draw conclusions of a physical nature is exhibited. Noll’s paper emerged from a report that he presented in a seminar at Indiana University in the summer of 1954. The seminar was organized by Clifford Truesdell, whose inspiration Noll gratefully acknowledged.


Continuum mechanical Statistical mechanical 

Mathematics Subject Classification (2000)

82C21 82C22 35Q82 80A17 74A15 


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  1. 1.
    Irving, J.H., Kirkwood, J.G.: The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18, 817–829 (1950) CrossRefMathSciNetADSGoogle Scholar
  2. 2.
    Schwartz, L.: Théorie des distributions. Hermann, Paris (1950) zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Richard B. Lehoucq
    • 1
    Email author
  • Anatole Von Lilienfeld-Toal
    • 2
  1. 1.Applied Mathematics & Applications DepartmentSandia National LaboratoriesAlbuquerqueUSA
  2. 2.Multiscale Dynamic Material Modeling DepartmentSandia National LaboratoriesAlbuquerqueUSA

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