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Nonequilibrium distribution functions in a fluid. (English) Zbl 0114.21404


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[1] Kirkwood, J. Chem. Phys. 14 pp 180– (1946)
[2] H. Grad,Encyclopedia of Physics, edited by S. Flügge (Springer-Verlag, Berlin, Germany, 1958), Vol. XII, p. 205.
[3] Frisch, J. Chem. Phys. 22 pp 1713– (1954)
[4] Bhatnager, Phys. Rev. 94 pp 511– (1954)
[5] Chandrasekhar, Rev. Modern Phys. 15 pp 1– (1943)
[6] S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases(Cambridge University Press, Cambridge, England, 1958). · Zbl 0063.00782
[7] Brout, Physica 23 pp 953– (1957)
[8] Brout, Physica 22 pp 621– (1956)
[9] Zwanzig, Phys. Fluids 2 pp 12– (1959)
[10] van Hove, Physica 21 pp 518– (1955) · Zbl 0074.22804
[11] Kirkwood, J. Chem. Phys. 17 pp 988– (1949)
[12] Zwanzig, J. Chem. Phys. 21 pp 2050– (1953)
[13] Zwanzig, J. Chem. Phys. 22 pp 783– (1954)
[14] Grad, Comm. Pure and Appl. Math. 2 pp 331– (1949)
[15] Grad, Comm. Pure and Appl. Math. 2 pp 325– (1949)
[16] This fact should prove useful in a systematic discussion of the existence and uniqueness of solutions of the Fokker-Planck equation.
[17] In the 20 moment approximation the presence of the force F modifies Eq. (5.14) of reference 13 for Sigk by introducing the extra term -Fipgkm to the right-hand side. Clearly this contribution must vanish in the 13 moment approximation since pkk = 0.
[18] Ono, Sci. Papers Coll. Gen. Educ. Univ. Tokyo 5 pp 87– (1955)
[19] I. Prigogine,Étude Thermodynamique des Phénomènes Irréversibles(Desoer, Liège, 1947), Chap. V.
[20] See also papers and references cited by M. J. Klein, H. Wergeland, and H. B. Callen inTransport Processes in Statistical Mechanics, edited by I. Prigogine (Interscience Publishers, Inc., New York, 1958).
[21] S. R. de Groot,Thermodynamics of Irreversible Processes(Interscience Publishers, Inc., New York, 1951). · Zbl 0045.27104
[22] H. S. Green,The Molecular Theory of Fluids(Interscience Publishers, New York, 1952).
[23] Actually, in the calculation of heat conductivity by Zwang et al. cited in footnote 11, g0 is considered to be a function of temperature and pressure and consideration is limited to stationary states of uniform pressure.
[24] Lebowitz, Phys. Rev. 114 pp 1192– (1959)
[25] This agrees with Lebowitz’s Eq. (5.5) when use is made of his Eq. (5.15) to identify {\(\eta\)} as -{\(\mu\)}kT.
[26] We note, however, that the Fokker-Planck equation associates different relaxation times with the kinetic and the potential parte of the heat flux; i.e., the relaxation times are {\(\tau\)}l = 1l{\(\zeta\)} wherelis the order of the Hermite polynomial in velocity. On the other hand, in reference 23 and in this section only a single relaxation for heat flow is assumed.
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