Abstract
On the basis of the scale covariance of correlation functions under a coarsegraining in space and time, the Boltzmann equation for neutral gases, the Balescu-Lenard-Boltzmann-Landau equation for dilute plasmas, and linear equations for the variances of fluctuations are derived from the BBGKY hierarchy equations with no short-range correlations at the initial time. This is done by using Mori's scaling method in an extended form. Thus it is shown that the scale invariance of macroscopic features affords a useful principle in nonequilibrium statistical mechanics. It is also shown that there existtwo kinds of correlation functions, one describing the interlevel correlations of the kinetic level with its sublevels and the other representing the fluctuations in the kinetic level.
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Partially financed by the Scientific Research Fund of the Ministry of Education.
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Morita, T., Mori, H. & Tokuyama, M. A scaling method for deriving kinetic equations from the BBGKY hierarchy. J Stat Phys 18, 137–153 (1978). https://doi.org/10.1007/BF01014305
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DOI: https://doi.org/10.1007/BF01014305