Abstract
The typical fluctuation of the net electric chargeQ contained in a subregionΛ of an infinitely extended equilibrium Coulomb system is expected to grow only as √S, whereS is the surface area ofΛ. For some cases it has been previously shown thatQ/√S has a Gaussian distribution as ¦Λ¦→∞. Here we study the probability law for larger charge fluctuations (large-deviation problem). We discuss the case when both ¦Λ¦ andQ are large, but now withQ of an order larger than √S. For a given value ofQ, the dominant microscopic configurations are assumed to be those associated with the formation of a double electrical layer along the surface ofΛ. The probability law forQ is then determined by the free energy of the double electrical layer. In the case of a one-component plasma, this free energy can be computed, for large enoughQ, by macroscopic electrostatics. There are solvable two-dimensional models for which exact microscopic calculations can be done, providing more complete results in these cases. A variety of behaviors of the probability law are exhibited.
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References
H. Van Bijeren and B. U. Felderhof,Mol. Phys. 38:1179 (1979).
Ch. Gruber, Ch. Lugrin, and Ph. A. Martin,J. Stat. Phys. 22:193 (1980).
Ph. A. Martin and T. Yalcin,J. Stat. Phys. 22:435 (1980).
W. Kunz, P. Calmettes, G. Jannink, L. Belloni, T. Cartailler, and P. Turq,J. Chem. Phys. 96:7034 (1992).
J. L. Lebowitz,Phys. Rev. A 27:1491 (1983).
E. H. Lieb and H. Narnhofer,J. Stat. Phys. 12:291 (1975).
A. Alastuey and B. Jancovici,J. Phys. (Paris)42:1 (1981).
B. Jancovici,Phys. Rev. Lett. 46:386 (1981).
B. Jancovici,J. Phys. Lett. (Paris)42:L223 (1981).
E. H. Lieb and J. L. Lebowitz,Adv. Math. 9:316 (1972).
M. L. Rosinberg and L. Blum,J. Chem. Phys. 81:3700 (1984).
F. Cornu and B. Jancovici,J. Chem. Phys. 90:2444 (1989).
B. Jancovici,J. Stat. Phys. 28:43 (1982).
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Jancovici, B., Lebowitz, J.L. & Manificat, G. Large charge fluctuations in classical Coulomb systems. J Stat Phys 72, 773–787 (1993). https://doi.org/10.1007/BF01048032
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DOI: https://doi.org/10.1007/BF01048032