  The Onsager reciprocal relations are established within the phenomenological
framework of the thermodynamics of irreversible processes. In order to do so,
the dissipated power densities associated to scalar and vectorial processes are
written as positive semi-definite quadratic forms of the corresponding
generalised forces, as required by the local expression of the second law in
the neighbourhood of the equilibrium. The antisymmetric part of the scalar and
vectorial Onsager matrices do not contribute to the dissipation, which yields
the scalar and vectorial Onsager reciprocal relations. Furthermore, the
positive semi-definite quadratic forms of the generalised scalar and vectorial
forces are invariant under time reversal, which yields the scalar and vectorial
Casimir-Onsager reciprocal relations, that are a generalisation of the Onsager
reciprocal relations.
