Abstract
In their stochastic versions, dynamical systems take the form of the linear dynamics of a probability distribution. We show that exact dimensional reduction of such systems can be carried out, and is physically relevant when the dimensions to be eliminated can be identified with those that represent transient behavior, disappearing under typical coarse graining. Application is made to non-uniform quasi-low dimensional diffusion, resulting in a systematic extension of the “classical” Fick-Jacobs approximate reduction to an exact subdynamics.
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References
See e.g. H. Schlichting, “Boundary Layer Theory,” Chaps Ie, VIII b. Mc Graw-Hill (1955).
N. N. Bogoliubov, “Problems of Dynamic Theory in Statistical Physics” in “Studies in Statistical Mechanics, Vol. 1,” (ed.) J de Boer and G.E. Uhlenbeck, North-Holland Pub, (1962).
H. Mori, Prog. Theor. Phys. (Kyoto) 34:423 (1965).
R. Zwanzig, in: “Lectures in Theoretical Physics,” Vol. 3, Interscience (1961).
V. I. Yudson and P. Reineker, Phys Rev E 64:031108 (2001).
M. H. Jacobs, “Diffusion Processess,” Springer (1967).
J. H. M. Wedderburn, “Lectures on Matrices,” Chap IX, secs 2,3, American Mathematical Society (1934).
P. Kalinay and J. K. Percus, J. Chem. Phys. 122:204701 (2005).
See e.g. N. G. Van Kampen, “Stochastic Processes in Physics and Chemistry,” North-Holland (1981).
R. Zwanzig, J. Phys. Chem. 96:3926 (1992).
R. Bowles, K. K. Mon, and J. K. Percus, J. Chem. Phys. 121:10668 (2004).
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Kalinay, P., Percus, J.K. Exact Dimensional Reduction of Linear Dynamics: Application to Confined Diffusion. J Stat Phys 123, 1059–1069 (2006). https://doi.org/10.1007/s10955-006-9081-3
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DOI: https://doi.org/10.1007/s10955-006-9081-3