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Published online by Cambridge University Press: 18 June 2021
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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