Abstract
Information theory is used to study the effects of screening on the rate of entropy production during pattern formation. Screening is an effect where the outermost parts of a growing fractal pattern influence the growth probability at interior sites. The results demonstrate that a state of maximum entropy production does exist for dynamical systems which generate patterns based on simple screening rules alone. This state corresponds to a critical point where the pattern exhibits self-similarity and fractal properties typical of random aggregates. Scaling occurs because the screening transmits information from the smallest to the largest scales of the system.
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References
T. A. Witten, Jr. and L. M. Sander,Phys. Rev. Lett. 47:1400 (1981).
B. B. Mandlebrot,The Fractal Geometry of Nature (Freeman, San Francisco, 1983).
J. H. Kaufman, A. I. Nazzal, O. R. Melroy, and A. Kapitulnik,Phys. Rev. B. 35:1881 (1987).
J. H. Kaufman, O. R. Melroy, F. F. Abraham, and A. I. Nazzal,Solid State Commun. 60:757 (1986).
L. Niemeyer, L. Pietronero, and H. J. Wiesmann,Phys. Rev. Lett. 52:1033 (1984).
A. Coniglio and H. E. Stanley,Phys. Rev. Lett. 52:1068 (1984).
P. Meakin, H. E. Stanley, A. Coniglio, and T. A. Witten,Phys. Rev. A 32:2364 (1985).
P. Bak, C. Tang, and K. Wiesenfeld,Phys. Rev. Lett. 59:381 (1987).
I. Prigogine, G. Nicolis, and A. Babloyantz,Phys. Today 25(11):23 (1972);Science 201:777 (1978).
S. Wolfram, inScaling Phenomena in Disordered Systems, R. Pynn and A. Skjeltorp, eds. (Plenum Press, New York, 1985).
C. E. Shannon and W. Weaver,The Mathematical Theory of Communication (University of Illinois Press, 1962).
D. L. Goodstein,States of Matter (Prentice-Hall, Englewood Cliffs, N.J., 1975), pp. 43–46.
R. Landauer,Phys. Today (November 1987);Phys. Rev. A 12:636 (1975).
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Kaufman, J.H., Melroy, O.R. & Dimino, G.M. The effect of screening on entropy production in pattern formation. J Stat Phys 55, 331–340 (1989). https://doi.org/10.1007/BF01042603
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DOI: https://doi.org/10.1007/BF01042603