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8. binary collision expansion

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6 - Basic Tools of Nonequilibrium Statistical Mechanics
J. R. Dorfman, University of Maryland, College Park, Henk van Beijeren, Universiteit Utrecht, The Netherlands, T. R. Kirkpatrick, University of Maryland, College Park
Book:

Contemporary Kinetic Theory of Matter

Published online:

18 June 2021

Print publication:

24 June 2021, pp 205-254
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Summary

Some fundamental techniques of kinetic theory for N-particle systems are introduced. In particular, binary collision operators and the binary collision expansion are defined for both smooth and hard sphere potentials. The Liouville equation for the phase space distribution 7 function is presented for smooth interaction potentials, and the pseudo-Liouville equation is given for hard sphere interactions. Integration of the Liouville or pseudo-Liouville equation over a number of particle variables leads to the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy equations. It is shown that the binary collision expansion is a correct representation of the dynamics of a system of N hard sphere particles. The Green-Kubo formulas for transport coefficients in terms of time correlation functions are derived.

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6 - Basic Tools of Nonequilibrium Statistical Mechanics

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6 - Basic Tools of Nonequilibrium Statistical Mechanics

Summary