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On the linearity of the self-diffusion process

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Abstract

Formal arguments are given that the self-diffusion process, understood as the mutual diffusion process in a system which consists of two mechanically similar species of particles, and which is at total equilibrium if the species labels are ignored, is an inherently linear, but nonlocal, transport process. There are no nonlinear Burnett effects, and the nonlocal diffusion coefficient is independent of the composition of the mixture. The present state of knowledge, from theory and from computer experiments, concerning the various quantities which appear in the formal analysis is summarized for both fluid and Lorentz systems.

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References

  1. W. W. Wood, inThe Boltzmann Equation, Theory and Applications, E. G. D. Cohen and W. Thirring, eds. (Acta Physica Austriaca, Suppl. X), (Springer, Berlin, 1973), p. 451.

    Google Scholar 

  2. J. L. Lebowitz and H. Spohn,J. Stat. Phys. 19:633 (1978).

    Google Scholar 

  3. J. R. Dorfman, inFundamental Problems in Statistical Mechanics III, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1975), p. 277.

    Google Scholar 

  4. B. J. Berne, inPhysical Chemistry, An Advanced Treatise, Vol. VIII-BLiquid State, D. Henderson, ed. (Academic Press, New York, 1971), p. 540.

    Google Scholar 

  5. J. A. McLennan,Phys. Rev. A 8:1479 (1973).

    Google Scholar 

  6. M. H. Ernst, B. Cichocki, J. R. Dorfman, J. Sharma, and H. van Beijeren,J. Stat. Phys. 18:237 (1978).

    Google Scholar 

  7. J. W. Dufty, private communication.

  8. N. G. van Kampen,Phys. Norwegica 5:10 (1971).

    Google Scholar 

  9. H. J. Raveche and J. E. Mayer,J. Chem. Phys. 52:3990 (1970).

    Google Scholar 

  10. L. van Hove,Phys. Rev. 95:249 (1954).

    Google Scholar 

  11. W. E. Alley and B. J. Alder,Phys. Rev. Lett. 43:653 (1979).

    Google Scholar 

  12. T. L. Hill,Statistical Mechanics, (McGraw-Hill, New York, 1956), p. 233.

    Google Scholar 

  13. B. J. Alder and T. E. Wainwright,Phys. Rev. Lett. 18:968 (1967);J. Phys. Soc. Jpn. 26 Suppl.:267 (1969), (Proc. Int. Conf. Stat. Mech., Kyoto, 1968);Phys. Rev. A 1:18 (1970).

    Google Scholar 

  14. G. Subramanian, D. Levitt, and H. T. Davis,J. Chem. Phys. 60:2 (1974); G. Subramanian and H. T. Davis,Phys. Rev. A 11:1430 (1975).

    Google Scholar 

  15. W. W. Wood, inFundamental Problems in Statistical Mechanics III, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1975), p. 331.

    Google Scholar 

  16. J. J. Erpenbeck and W. W. Wood, inStatistical Mechanics, Part B: Time-Dependent Processes, B. J. Berne, ed. (Vol. 6 ofModern Theoretical Chemistry, W. H. Miller, H. F. Schaefer III, B. J. Berne, and G. A. Segal, eds.), (Plenum, New York, 1977), p. 1.

    Google Scholar 

  17. D. Levesque and W. T. Ashurst,Phys. Rev. Lett. 33:277 (1974).

    Google Scholar 

  18. S. Toxvaerd,Phys. Rev. Lett. 43:529 (1979).

    Google Scholar 

  19. J. R. Dorfman and E. G. D. Cohen,Phys. Rev. Lett. 25:1257 (1970);Phys. Rev. A 6:776 (1972);12:292 (1975).

    Google Scholar 

  20. M. H. Ernst, E. H. Hauge, and J. M. J. van Leeuwen,Phys. Rev. Lett. 25:1254 (1970);Phys. Lett. 34A:419 (1971);Phys. Rev. A 4:2055 (1971);J Stat. Phys. 15:7, 23 (1976).

    Google Scholar 

  21. Y. Pomeau and P. Resibois,Phys. Rev. 19:63 (1975).

    Google Scholar 

  22. J. R. Dorfman and H. van Beijeren, inStatistical Mechanics, Part B: Time-Dependent Processes, B. J. Berne, ed. (Plenum, New York, 1977), p. 65.

    Google Scholar 

  23. S. Yip,Ann. Rev. Phys. Chem. 30:547 (1979).

    Google Scholar 

  24. H. van Beijeren and M. H. Ernst,J. Stat. Phys. 21:125 (1979).

    Google Scholar 

  25. J. R. Dorfman,Studies in Statistical Mechanics, Vol. IXPerspectives in Statistical Physics (North-Holland, Amsterdam, 1981).

    Google Scholar 

  26. J. P. Hansen, D. Levesque, and J. J. Weis,Phys. Rev. Lett. 43:979 (1979).

    Google Scholar 

  27. I. M. de Schepper and M. H. Ernst,Physica 87A:35 (1977).

    Google Scholar 

  28. T. E. Wainwright, B. J. Alder, and D. M. Gass,Phys. Rev. A 4:233 (1971).

    Google Scholar 

  29. W. T. Ashurst and W. G. Hoover,Phys. Rev. Lett. 31:206 (1973);Phys. Rev. A 11:658 (1975).

    Google Scholar 

  30. J. L. Lebowitz and H. Spohn, private communication.

  31. M. H. Ernst and A. Weyland,Phys. Lett. 34A:39 (1971).

    Google Scholar 

  32. C. Bruin,Phys. Rev. Lett. 29:1670 (1972);Physica 72:261 (1974).

    Google Scholar 

  33. J. C. Lewis and J. A. Tjon,Phys. Lett. 66A:349 (1978).

    Google Scholar 

  34. B. J. Alder and W. E. Alley,J. Stat. Phys. 19:341 (1978).

    Google Scholar 

  35. B. J. Alder, inLecture Notes in Physics, Vol. 84, L. Garrido, P. Seglar, and P. J. Shepherd, eds. (Springer, Berlin, 1978), p. 169.

    Google Scholar 

  36. W. E. Alley, thesis Studies in Molecular Dynamics of the Friction Coefficient and the Lorentz Gas, University of California, Lawrence Livermore National Laboratory, Livermore, California, 1979.

    Google Scholar 

  37. L. A. Bunimovich and Y. G. Sinai,Commun. Math. Phys. 78:479 (1981); Y. G. Sinai,Ann. N.Y. Acad. Sci., Nonlinear Dynamics (1980), p. 143.

    Google Scholar 

  38. I. M. de Schepper, H. van Beijeren, and M. H. Ernst,Physica 75:1 (1974); I. M. de Schepper, thesis Generalized Hydrodynamics of the Diffusion Process, Nijmegen (1974); I. M. de Schepper and M. H. Ernst,Physica 93A:611 (1978).

    Google Scholar 

  39. I. M. de Schepper and M. H. Ernst,Physica 98A:189 (1979).

    Google Scholar 

  40. T. Keyes and I. Oppenheim,Physica 70:100 (1973); H. H-H. Yuan and I. Oppenheim,Ibid. 90A:1, 21, 561 (1978).

    Google Scholar 

  41. J. W. Dufty and J. A. McLennan,Phys. Rev. A 9:1266 (1974).

    Google Scholar 

  42. B. J. Alder, private communication.

  43. M. H. Ernst and H. van Beijeren,J. Stat. Phys.,26:1 (1981).

    Google Scholar 

  44. J. L. Lebowitz, inStatistical Mechanics: New Concepts, New Problems, New Applications, S. A. Rice, K. F. Freed, and J. C. Light, eds. (University of Chicago Press, Chicago, 1972), p. 41.

    Google Scholar 

  45. J. J. Erpenbeck and W. W. Wood,J. Stat. Phys.,24:455 (1981).

    Google Scholar 

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Work performed under contract with the U.S. Department of Energy.

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Wood, W.W., Erpenbeck, J.J. On the linearity of the self-diffusion process. J Stat Phys 27, 37–56 (1982). https://doi.org/10.1007/BF01011738

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