Phenomenological Macroscopic Symmetry in Dissipative Nonlinear Systems

Abstract

We show that systems whose equations of motion are derivable from a Lagrangian formulation extended to allow for dissipative effects by the inclusion of dissipative forces of the form (resistance X flow) and subject to constraints expressing conservation of quantities such as mass and charge possess a symmetry property at stationary states arbitrarily far from thermodynamic equilibrium. Examples of such systems are electrical networks] discrete mechanical systems and systems of chemical reactions. The symmetry is in general only an algebraic one, not the differential Onsager reciprocity valid close to equilibrium; the more general property does reduce to the Onsager result in the equilibrium limit, however. No restrictions are placed on the form of the resistances for dissipative processes; they may have arbitrary dependencies on the state of the system and/or its flows. Thus, the symmetry property is not limited to linear systems. The approach presented here leads naturally to the proper set of flows and forces for which the Onsager-like symmetry holds.