On nonlinear Onsager symmetry and mass-action kinetics

Abstract

ABSTRACT This brief paper is a continuation of previous work (J.D. Goddard, “Dissipation potentials for reaction-diffusion systems.” I&EC Res.,54.16,4078–4083, 2015) dealing with the application of Edelen’s dissipation potentials to the irreversible thermodynamics of chemical-reaction networks. It is shown that one can achieve non-linear Onsager symmetry by means of constraints on a certain combination of Gibbs free energies dubbed reactivity, from which it follows that reaction rates are given simply as gradients of a dissipation potential. This may open the door to the application of thermodynamics and variational methods to combustion and biochemical reaction networks, including the possibility of enhanced derivation of reduced kinetic mechanisms. A graph-theoretical description of reaction networks is presented, which is based on stoichiometric hypergraphs and encompasses several past treatments in a more economical fashion. It may also suggest hypergraph optimization techniques to enhance the selection of reduced mechanisms.