Abstract
The exact form for the kinetic equation derived by Mori, Fujisaka, and Shigematsu (MFS) is used to obtain several approximations better suited to be compared with macroscopic transport equations. Three approximations are discussed, namely, those known as the diagonal, the slow process, and the Markovian. The corresponding results are emphasized and their relationship is established. In particular, the Kramers-Moyal expansion for the Markovian kinetic equation is obtained from a microscopic basis.
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del Rio, J.L., García-Colín, L.S. A unified approach for deriving kinetic equations in nonequilibrium statistical mechanics. II. Approximate results. J Stat Phys 19, 109–127 (1978). https://doi.org/10.1007/BF01012506
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DOI: https://doi.org/10.1007/BF01012506