Abstract
In the McKean model the BBGKY hierarchy is equivalent to a simple hierarchy of coupled equations for thep-particle correlation functions. Approximate solutions are obtained by truncating the hierarchy. The convergence of the truncation method is studied by comparison with the exact solution for the model, which can be given in closed form. In the long-time limit the exact solution is linearized around the equilibrium value, showing the decay of the correlations. It turns out thatp-particle correlations decayp times faster than the nonequilibrium one-particle distribution.
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References
R. Balescu,Equilibrium and Non-Equilibrium Statistical Mechanics (Wiley, New York, 1975).
N. N. Bogoliubov, inStudies in Statistical Mechanics, J. de Boer and G. R. Uhlenbeck, eds. (North-Holland, Amsterdam, 1962), Vol. 1, pp. 71ff.
F. Henin,Physica 76:201 (1974).
H. Spohn, inNonequilibrium Phenomena I, J. L. Lebowitz and E. W. Montroll, eds. (North-Holland, Amsterdam, 1983).
H. Spohn, inProceedings CIME School, Kinetic Theories and the Boltzmann Equation, C. Cercignani, ed. (Montecatini, 1981).
O. E. Lanford, inDynamical Systems and Applications, J. Moser, ed. (Lecture Notes in Physics, Vol. 38, Springer, Berlin, 1975).
M. Kac, inThe Boltzmann Equation, Theory and Applications, E. G. D. Cohen and W. Thirring, eds. (Springer-Verlag, New York, 1973).
H. P. McKean, Jr.,J. Comb. Theory 2:358 (1967).
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Schmitt, K.J. N-particle correlations in the McKean model. J Stat Phys 46, 283–302 (1987). https://doi.org/10.1007/BF01010347
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DOI: https://doi.org/10.1007/BF01010347