Onsager Reciprocal Relations and Detailed Balance
Let the principle of detailed balance be valid. Then, in the linear approximation near equilibrium the reaction rates for the generalized mass action law are
Therefore, in the linear approximation near equilibrium, the kinetic equations are :
This is exactly the Onsager form: following the original work of Onsager, we should introduce the thermodynamic forces and the matrix of coefficients in the form
The coefficient matrix is symmetric:
These symmetry relations, are exactly the Onsager reciprocal relations. The coefficient matrix is non-positive. It is negative on the linear span of the stoichiometric vectors .
So, the Onsager relations follow from the principle of detailed balance in the linear approximation near equilibrium.
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