Functional Random-Walk Model of the Many-Particle System
- 1 February 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (2) , 657-666
- https://doi.org/10.1063/1.1665180
Abstract
By Fourier‐transforming the author's recently proposed state functional formalism for the BBGKY hierarchy, a new perspective of nonequilibrium statistical mechanics is given: the basic equation is formally very close to the Fokker‐Planck equation and may readily be modified to a universal master equation (with irreversibility) by a slight change. Hence, the problem reduces to one of a generalized random‐walk such that the stochastic quantity to be considered is the particle‐number density in the 1‐body phase space. A general solution is formulated for the weak interaction case.Keywords
This publication has 14 references indexed in Scilit:
- Functional Methods in Statistical Mechanics. I. Classical TheoryJournal of Mathematical Physics, 1969
- Direct Computation of the Functional Integral Expression for the Correlation Function of the Turbulent Velocity FieldPhysics of Fluids, 1968
- General Solution for the Modified Bogoliubov Functional in Non-Equilibrium Statistical MechanicsProgress of Theoretical Physics, 1968
- Functional Approach to Classical Non-Equilibrium Statistical MechanicsJournal of Mathematical Physics, 1967
- General Solution for the Modified Bogoliubov Functional in Non-Equilibrium Statistical MechanicsProgress of Theoretical Physics, 1966
- Uniqueness of Steady-State Solutions to the Fokker-Planck EquationJournal of Mathematical Physics, 1965
- Irreversible processes in gases: III. Inhomogeneous systemsPhysica, 1960
- Irreversible processes in gases I. The diagram techniquePhysica, 1959
- A general kinetic theory of liquids I. The molecular distribution functionsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1946
- Zur Theorie der stetigen zuf lligen ProzesseMathematische Annalen, 1933