Symmetry relations for the conductivity tensor

A long-standing weakness in the theoretical analysis of reciprocity relations is eliminated. The Onsager reciprocity theorem demonstrates the symmetry of phenomenological coefficients for systems described by a discrete set of variables. It has previously been demonstrated that this theorem implies that the divergence of the generalized conductivity tensor is symmetric. After some additional analysis it has been argued that the symmetry of the tensor itself is implied. This argument has been criticized in the literature. In the present paper it is shown that, when boundary conditions are appropriately incorporated into the analysis, one obtains the symmetry of the conductivity tensor from the Onsager relations.