Abstract
A new method to obtain a series of reduced dynamics at various stages of coarse-graining is proposed. This ranges from the most coarse-grained one which agrees with the deterministic time evolution equation for averages of the relevant variables to the least coarse-grained one which is the generalized Fokker-Planck equation for the probability distribution function of the relevant variables. The method is based on the extention of the Kawasaki-Gunton operator with the help of the principle of maximum entropy.
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References
J.-L. Barrat and J.P. Hansen, Basic Concepts for Simple and Complex Liquids, Cambridge: {Cambridge} University Press (2003).
T.A. Witten, Structured Fluids, Oxford: Oxford University Press (2004).
R. Evans, Adv. Phys. 28:143 (1979).
R. Evans, in Fundamentals of Inhomogeneous Fluids, ed. D. Henderson, New York: Dekker, chapter 3 (1992).
U. M. B. Marconi and P. Tarazona, J. Chem. Phys. 110:8032 (1999).
U. M. B. Marconi and P. Tarazona, J. Phys. Condens. Matter 12:A413 (2000).
A. J. Archer and R. Evans, J. Chem. Phys. 121:4246 (2004).
D. Reinel and W. Dieterich, J. Chem. Phys. 104:5234 (1996).
H. P. Fischer, J. Reinhard, W. Dieterich, J.-F. Gouyet, P. Maass, A. Majhofer, and D. Reinel, J. Chem. Phys. 108:3028 (1998).
M. Kessler, W. Dieterich, H. L. Frisch, J.-F. Gouyet, and P. Maass, cond-mat/0201456.
D. S. Dean, J. Phys. A 29:L613 (1996).
K. Kawasaki, Physica A 208:35 (1994).
A. Yoshimori, Phys. Rev. E 59:6535 (1999).
A. Yoshimori, Phys. Rev. E 71:031203 (2005).
H. Frukawa and R. Hayakawa, J. Phys. A 33:L135 (2000).
A. J. Archer and M. Rauscher, J. Phys. A 37:9325 (2004).
K. Kawasaki, Physica A 362:249 (2006).
J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids, London: Academic Press (1986)
D. Zubarev, V. Morozov, and G. Röpke, Statistical Mechanics of Nonequilibrium Processes, Berlin: Akademie Verlag (1996)
K. Kawasaki and J. D. Gunton, Phys. Rev. A 8:2048 (1973).
E. Jaynes, Papers on Probability, Statistics, and Statistical Physics, ed. R. Rosenkrantz, D. Reidel Publishing Company (1983).
P. Mazur, Physica A 261:451 (1998).
H. A. Kramers, Physica 7:284 (1940).
S. P. Das and G. F. Mazenko, Phys. Rev. A 34:2265 (1986).
R. Graham, in Functional Integration, eds. Antoine and Terapegui, New York: Plenum (1980).
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Kawasaki, K. Principle of Maximum Entropy and Reduced Dynamics. J Stat Phys 123, 711–740 (2006). https://doi.org/10.1007/s10955-006-9121-z
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DOI: https://doi.org/10.1007/s10955-006-9121-z