text: Let the principle of detailed balance be valid. Then, for small deviations from equilibrium, the kinetic response of the system can be approximated as linearly related to its deviation from chemical equilibrium, giving the reaction rates for the generalized mass action law as:
  Therefore, again in the linear response regime 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.