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 TMF, 1972, Volume 13, Number 3, Pages 406–420 (Mi tmf3277)

Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy

D. N. Zubarev, M. Yu. Novikov

Abstract: A generalized formulation of the boundary condition of correlation weakening for the Liouville equation is presented; it is based on the introduction of an infinitesimally small source that breaks the symmetry of this equation under time reversal. This leads to the BBGKY hierarchy of equations with boundary conditions for all the reduced distribution functions except the first or except the first and second. It is shown that, irrespective of the existence of a small parameter, one can obtain closed kinetic equations for the single-particle or the twoparticle distribution function.

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English version:
Theoretical and Mathematical Physics, 1972, 13:3, 1229–1238

Citation: D. N. Zubarev, M. Yu. Novikov, “Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy”, TMF, 13:3 (1972), 406–420; Theoret. and Math. Phys., 13:3 (1972), 1229–1238

Citation in format AMSBIB
\Bibitem{ZubNov72} \by D.~N.~Zubarev, M.~Yu.~Novikov \paper Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy \jour TMF \yr 1972 \vol 13 \issue 3 \pages 406--420 \mathnet{http://mi.mathnet.ru/tmf3277} \transl \jour Theoret. and Math. Phys. \yr 1972 \vol 13 \issue 3 \pages 1229--1238 \crossref{https://doi.org/10.1007/BF01036148} 

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This publication is cited in the following articles:
1. M. Yu. Novikov, “Master equation and Bogolyubov's method of functional expansions”, Theoret. and Math. Phys., 16:3 (1973), 920–928
2. R. M. Yul'met'yev, “Investigation of invariants of a many-particle system by the method of projection operators”, Theoret. and Math. Phys., 20:3 (1974), 914–922
3. D. N. Zubarev, M. Yu. Novikov, “Diagram method of constructing solutions of Bogolyubov's chain of equations”, Theoret. and Math. Phys., 18:1 (1974), 55–62
4. L. Ts. Adzhemyan, F. M. Kuni, T. Yu. Novozhilova, “Nonlinear generalization of Mori's method of projection operators”, Theoret. and Math. Phys., 18:3 (1974), 274–280
5. A. V. Prozorkevich, S. A. Smolyanskii, “Derivation of relativistic transport equations of a plasma in a strong electromagnetic field”, Theoret. and Math. Phys., 23:3 (1975), 608–614
6. R. M. Yul'met'yev, “Bogolyubov's abridged description of equilibrium systems and derivation of an equation for the radial distribution function in a liquid”, Theoret. and Math. Phys., 25:2 (1975), 1100–1108
7. D. N. Zubarev, A. M. Khazanov, “Generalized Fokker–Planck equation and construction of projection operators for different methods of reduced description of nonequilibrium states”, Theoret. and Math. Phys., 34:1 (1978), 43–50
8. D. N. Zubarev, V. G. Morozov, “Formulation of boundary conditions for the BBGKY hierarchy with allowance for local conservation laws”, Theoret. and Math. Phys., 60:2 (1984), 814–820
9. E. F. Popov, “Statistical description of a system of charged particles”, Theoret. and Math. Phys., 76:3 (1988), 981–989
10. D. N. Zubarev, V. G. Morozov, I. P. Omelyan, M. V. Tokarchuk, “Kinetic equations for dense gases and liquids”, Theoret. and Math. Phys., 87:1 (1991), 412–424
11. Tarasov, VE, “Fokker-Planck equation for fractional systems”, International Journal of Modern Physics B, 21:6 (2007), 955
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