Geodesic
Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 3, pp. 406-420

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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. 
@article{TMF_1972_13_3_a10,
     author = {D. N. Zubarev and M. Yu. Novikov},
     title = {Generalized formulation of the boundary condition for the {Liouville} equation and for the {BBGKY} hierarchy},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {406--420},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1972_13_3_a10/}
}
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D. N. Zubarev; M. Yu. Novikov. Generalized formulation of the boundary condition for the Liouville equation and for the BBGKY hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 13 (1972) no. 3, pp. 406-420. http://geodesic.mathdoc.fr/item/TMF_1972_13_3_a10/