Thermodynamic and Stochastic Theory of Reaction Diffusion Systems

So far we have considered only homogeneous reaction systems in which concentrations are functions of time only. Now we turn to inhomogeneous reaction systems in which concentrations are functions of time and space. There may be concentration gradients in space and therefore diffusion will occur. We shall formulate a thermodynamic and stochastic theory for such systems [1] first we analyze one-variable systems and then two- and multi-variable systems, with two or more stable stationary states, and then apply the theory to study relative stabihty of such multiple stable stationary states. The thermodynamic and stochastic theory of diffusion and other transport processes is given in Chap. 8. 

Let us take a one-variable system, such as the Schlogl model 

For inhomogeneous systems the number densities (concentrations) are functions of time and spatial coordinates. In a one-dimensional system with spatial coordinate 2 we discretize the space into many boxes, labelled with. .. — 1, i, + 1, see Fig. 5.1. 

The increase and decrease of the number of particles Xi are due to reaction and diffusion into and out of box i and can be written 

5 Thermodynamic and Stochastic Theory of Reaction-Diffusion Systems 

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Thermodynamic and Stochastic Theory of Reaction—Diffusion Systems Relative Stability of Multiple Stationary States... 

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