Generalised concentration fluctuations under diffusion equilibrium

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.