A STATISTICAL THEORY OF TRANSPORT PHENOMENA
A systematic procedure for the derivation of transport equations from the Liouville equation through the use of the BBGKY (Bogoliubov-Born- Green- Kirkwood-Yvon) hierarchy is put forward. The unique feature of the analysis is the use of statistical considerations to determine the method of truncating the hierarchy. A variational technique for the performance of Gibbs' ensemble average, which amounts essentially to an a priori assumption of an H-theorem, is used to determine the missing information when a lower member of the BBGKY hierarchy is substituted for the Liouville equation. The procedure is illustrated for the case of truncation at the lowest level in the hierarchy, and in a certain approximation the Fokker-Planck equation is recovered. However, in order to effect a complete evaluation of the coefficients of the Fokker-Planck term at this level, it is found that a physical principle that is implicit in the Fokker-Planck coefficients must be postulated. A discussion of this feature and a proposed experimental check on the analysis are given. (auth)
- Research Organization:
- Univ. of California, Livermore
- NSA Number:
- NSA-17-006818
- OSTI ID:
- 4733567
- Journal Information:
- Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 20; ISSN APNYA
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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