https://doi.org/10.1140/epjst/e2008-00756-1
Chemical reactions and fluctuations
Exact substitute processes for diffusion-reaction systems with exclusion rules
Department of Physics, Albert-Einstein University of Ulm, 89069 Ulm, Germany
Corresponding author: michael.schulz@uni-ulm.de
Lattice systems with one species diffusion-reaction processes under local complete exclusion rules are studied analytically. We discuss a rigorously derived Fokker-Planck equation for a so-called pseudo-probability. This probability distribution depends on continuous variables in contrast to the original discrete master equation, and their stochastic dynamics may be interpreted as a substitute process which is completely equivalent to the original lattice dynamics. Especially, averages and correlation functions of the continuous variables are connected to corresponding lattice quantities by simple relations. Although the substitute process for diffusion-reaction systems with exclusion rules has some similarities to the well known substitute process for the same system without exclusion rules, their exist a set of remarkable differences. The given approach is not only valid for the discussed single species processes. We give sufficient arguments that arbitrary combinations of uni-molecular and bimolecular lattice reactions under complete local exclusions may be described in terms of our approach.
© EDP Sciences, Springer-Verlag, 2008
