The stochastic Boltzmann equation and hydrodynamic fluctuations |
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Authors: | Hiroshi Ueyama |
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Affiliation: | (1) Max-Planck Institut für Festkörperforschung, Stuttgart, West Germany;(2) Present address: Department of Physics, College of General Education, Osaka University, Toyonaka, Japan |
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Abstract: | Based on the assumption of a kinetic equation in space, a stochastic differential equation of the one-particle distribution is derived without the use of the linear approximation. It is just the Boltzmann equation with a Langevin-fluctuating force term. The result is the general form of the linearized Boltzmann equation with fluctuations found by Bixon and Zwanzig and by Fox and Uhlenbeck. It reduces to the general Landau-Lifshitz equations of fluid dynamics in the presence of fluctuations in a similar hydrodynamic approximation to that used by Chapman and Enskog with respect to the Boltzmann equation.This work received financial support from the Alexander von Humboldt Foundation. |
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Keywords: | Stochastic differential equation Langevin equation Boltzmann equation hydrodynamic fluctuations master equation kinetic equation hard-sphere system |
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