Geodesic
Nonequilibrium fluctuations in a gas
Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 1, pp. 109-123
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Calculation is carried out of non-equilibrium fluctuations in the Boltzmann gas on ihe basis of the equation for smoothed distribution function for all particles of the system. This equation implies the chain of equations for distribution function obtained earlier in the works [1, 2, 4]. The calculation is also performed of the space-time spectral function of particle density fluctuations in phase space for weakly non-stationary and weakly non-homogeneous gas states, taking into account the “polarization” effects due to collective motion of atoms. It is shown that slow (in the periods of the free run order) fluctuations give rise to additional contribution into kinetic equation and to corresponding changes in gas dynamics equations. 
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Yu. L. Klimontovich. Nonequilibrium fluctuations in a gas. Teoretičeskaâ i matematičeskaâ fizika, Tome 9 (1971) no. 1, pp. 109-123. http://geodesic.mathdoc.fr/item/TMF_1971_9_1_a8/

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