What kinds of models are relevant

Spatio-temporal change of the quantities of components of chemically reactive mixtures are described by reaction-diffusion equations. These equations may be induced from reaction kinetics, when the diffusion of chemical substances is also involved, or deduced from a general theory of mixtures, when only mass-conservation is taken into account. (For theories of reactive mixtures in the deterministic, continuum context offered by the school of rational thermodynamics see, for example, Bowen (1969) or Samohyl (1982)). 

Both deterministic and stochastic models exist to describe reaction-diffusion systems macroscopically. Deterministic, continuum models are used frequently. (A mathematically thorough book, written for mathematicians interested in chemical and biological applications, is Fife (1979).) The main assumptions of applicability of this model are  

The assumptions just mentioned are most plausible in the thermodynamic limit, for example, just in the situation when CCD models of chemical kinetics are adequate. The basic equation to describe the temporal change of the vector p of spatial density functions p,  

The stochastic approach to reaction-diffusion systems is not mathematically well-established. Though spatio-temporal stochastic phenomena ought to be associated with random fields, and not with stochastic processes, the usual investigation of such kinds of physicochemical problems starts from the master equation, and then it is extended by some heuristic procedure. From the physical point of view the role of spatial fluctuations is obviously important. It is well known that the density fluctuations are spatially correlated, and according to the modern theory of critical phenomena (e.g. Fisher, 1974 Wilson Kogut, 1974) small fluctuations are amplified owing to spatial interactions causing drastic macroscopic effects. 

Some possibilities for defining stochastic models of reaction-diffusion systems will be shortly studied. The connection between deterministic and certain stochastic models that can be established by the extension of Kurtz theorems will be mentioned (Arnold, 1980 Arnold Theodosopulu, 1980). 

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