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Generalised concentration fluctuations under diffusion equilibrium

Published online by Cambridge University Press:  14 July 2016

Harold Ruben
Harold Ruben*
Affiliation:
University of Minnesota
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Abstract

Smoluchowski's classical analysis of the temporal fluctuation, under diffusion equilibrium, of the number of particles in a fixed region R of space is generalised to a set of disjoint regions; specifically, the single Smoluchowski region is divided into a finite number of non-intersecting subregions. The generalisation allows a more rigorous test of some of the consequences of the Einstein-Smoluchowski theory of Brownian motion to be carried out, and at the same time enables the Avogadro constant to be estimated with greater precision than is possible with the single region. In particular, the reversibility paradox of Loschmidt and the recurrence paradox of Zermelo are reexamined from the point of view of the fluctuation of configurations (a configuration being defined as the set of occupation numbers for the various subregions) rather than that of total concentration for the single region.

Type
Research Papers
Information
Journal of Applied Probability , Volume 1 , Issue 1 , June 1964 , pp. 47 - 68
Copyright
Copyright © Applied Probability Trust 1964 

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References

[1] Bartlett, M. S. (1950) Recurrence times. Nature 165, 727.Google Scholar
[2] Bartlett, M. S. (1956) An Introduction to Stochastic Processes. Cambridge University Press.Google Scholar
[3] Chandrasekhar, S. (1943) Stochastic problems in physics and astronomy. Rev. Mod. Phys. 15, 1–89. [Republished in Selected Papers on Noise and Stochastic Processes, 1954, Dover Publications, New York.] Google Scholar
[4] Doob, J. L. (1942) The Brownian movement and stochastic equations. Ann. Math. 43, 351–369.Google Scholar
[5] Fürth, R. (1918) Statistik und Wahrscheinlichkeitsnachwirkung. Phys. Zeit. 19, 421–426.Google Scholar
[6] Fürth, R. (1919) Statistik und Wahrscheinlichkeitsnachwirkung. Phys. Zeit. 20, 21.Google Scholar
[7] Kac, Mark (1959) Probability and Related Topics in Physical Sciences. Interscience Publishers, London.Google Scholar
[8] Smoluchowski, M. V. (1916) Drei Vorträge über Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen. Phys. Zeit. 17, 557–585.Google Scholar