Variants of kinetic constraints formalization

The section addresses the problem of specifying constraints (10), (16), (27), (32), and (40) on macroscopic kinetics as applied to various problems. Formalization of these constraints as well as constructions of MEIS are on the whole based on the Boltzmann assumption on the equilibrium of kinetic trajectories of motion toward point xeq and the possibility to describe them by autonomous equations of the form x - f(x). 

Three approaches can be outlined to choose the formalized thermodynamic description of the kinetic block of model (7)-(12) (1) the thermodynamic approach, with additional thermodynamic relations that limit some stages of the studied process mechanism, to be written (2) the approach related to the transformation of right-hand sides of the kinetic equations and transition from the space of sought variables of the solved problem to the space of thermodynamic potentials, and (3) the approach based on direct use of these sides. 

Applicability of the first approach suggested by Keiko and Zarod-nyuk is based on the unity of thermodynamics and kinetics which explain differently the same physical regularities. As was said above this unity was brilliantly revealed by Boltzmann in his kinetic and thermodynamic explanations of the second law. In our case, setting, for example, a constraint on the equilibrium constant value of an individual reaction S VjXj = 0 within complex chemical process and writing this constraint intone of the possible forms  

We will explain this method on the example of setting the constraint on the rate of the z-th chemical reaction. Let the rate equation of this reaction have the form  

The simplest situation in the use of the third method is when the constraint on the process rate is determined only by one reaction, for example, of form (46). In this case to find the limiting concentration (or another parameter of the r-th component) we can write the inequality  

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