**Dissipation in Systems With Semi-detailed Balance**

Let us represent the generalized mass action law in the equivalent form: the rate of the elementary process

is

where is the chemical potential and is the Helmholtz free energy. The exponential term is called the *Boltzmann factor* and the multiplier is the kinetic factor. Let us count the direct and reverse reaction in the kinetic equation separately:

An auxiliary function of one variable is convenient for the representation of dissipation for the mass action law

This function may be considered as the sum of the reaction rates for *deformed* input stoichiometric coefficients . For it is just the sum of the reaction rates. The function is convex because .

Direct calculation gives that according to the kinetic equations

This is *the general dissipation formula for the generalized mass action law*.

Convexity of gives the sufficient and necessary conditions for the proper dissipation inequality:

The semi-detailed balance condition can be transformed into identity . Therefore, for the systems with semi-detailed balance .

Read more about this topic: Detailed Balance

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