Classical Statistical Mechanics

  • James Glimm
  • Arthur Jaffe


Statistical mechanics is the bridge between molecular science and continuum mechanics. The input to statistical mechanics is a force law between particles. The particles can be atoms in a crystal, molecules in a gas or liquid, electrons in a plasma, amino acid units in a protein, elementary constituents in a complex polymer, etc. The forces between particles originate from Coulomb forces between electric charges and from magnetic dipole forces between magnetic moments. The classical force laws may be modified by the quantum mechanics (especially the Pauli exclusion principle) describing the particles. Normally the force laws are quite complicated and are not given by a simple analytical expression. Rather, they are given in one or more of the following four ways: (1) In terms of an unknown function, for which qualitative properties are postulated as laws of physics. (2) As a specific function, such as the Lennard-Jones potential or hard sphere potential. Such functions are chosen because they have representative features in common with the true force laws; for example, they may be asymptotically exact in some limiting region. (3) As a result of numerical calculation, based e.g. on the complicated exact force law and a Hartree-Fock approximation. (4) As a result of experimental measurement.


Ising Model Canonical Ensemble Heat Bath Helmholtz Free Energy Classical Ensemble 
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  1. [Friedman, 1962], [Huang, 1963], [Uhlenbeck and Ford, 1963], [Ruelle, 1969], [Lanford, 1973], [Thompson, 1980].Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • James Glimm
    • 1
  • Arthur Jaffe
    • 2
  1. 1.Courant Institute for Mathematical SciencesNew York UniversityNew YorkUSA
  2. 2.Harvard UniversityCambridgeUSA

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