N-port reciprocity and irreversible thermodynamics

The relation between the reciprocity of electrical networks and the thermodynamic Onsager-Casimir reciprocity is discussed, and the meaning of this relation for the theory of thermal noise in electrical networks is explained. Onsager-Casimir reciprocity is used in thermodynamic proofs of Nyquist´s theorem for the description of thermal resistor noise. When a thermodynamic interpretation of electrical networks is at hand, the reciprocity of linear networks and Onsager-Casimir reciprocity are (basically) equivalent. Assuming certain restrictions on current controlled nonlinear inductors and voltage controlled nonlinear capacitors, this equivalence can be generalized to networks with nonlinear dynamical elements. Onsager-Casimir reciprocity is a consequence of network reciprocity in case of nonlinear networks, when only situations in the neighbourhood of equilibrium are considered. In nonlinear systems, far from equilibrium, Onsager-Casimir reciprocity is not valid. The crucial point is the interpretation of electrical circuits as thermodynamic systems. Once this has been done, the relation between both types of reciprocity is obvious