Symmetric matrices implications

Onsager s reciprocal relations state that, provided a proper choice is made for the flows and forces, the matrix of phenomenological coefficients is symmetrical. These relations are proved to be an implication of the property of microscopic reversibility , which is the symmetry of all mechanical equations of motion of individual particles with respect to time t. The Onsager reciprocal relations are the results of the global gauge symmetries of the Lagrangian, which is related to the entropy of the system considered. This means that the results in general are valid for an arbitrary process. 

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