Exact Solution for Chemical Reactions

Consider a general reaction network with ideal mass-action laws of kinetics 

In these equations, A , u = 1. are stable species with concentrations au,u = 1. Sa kept constant by interactions with a set of reservoirs connected to the system, and = 1. are reaction intermediates with 

The entropy production rate is the sum of the product of the net flux times the affinity for each elementary reaction step (compare with the form 

The entropy production depends only on concentrations but not explicitly on time. The differential of the entropy production can be evaluated with the use of (12.23) 

For a stationary state x = x the net reaction rates of the active species equals zero and the first sum in the second of the equations in (12.24) is 

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