On nonlinear Onsager symmetry and mass-action kinetics

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.

KEYWORDS:

• Strictly dissipative systems
• non-dissipative fluxes
• non-linear Onsager symmetry
• variational methods
• mass-action kinetics
• combustion reactions
• reduced kinetic mechanisms
• directed & weighted hypergraphs

Acknowledgments

It is a distinct privilege and pleasure to offer the above paper as a tribute to the memory of Professor Paul A. Libby, renowned researcher and respected departmental colleague, with whom I became a close friend over the thirty year period from June 1991 until his demise in November of 2021. Although emeritus professor during that period, he maintained an admirable level of scientific activity, collaborating with various visitors from abroad. Paul was also participant in a daily coffee klatch, involving myself and two or three other colleagues in wide-ranging discussion of politics, history, and science. As perhaps the most serious-minded of the group Paul strove, sometimes without success, to keep our discussions on a high plane, adjourning the gathering with coffee cup as gavel whenever he felt we might be more productively engaged at our offices.

Beyond the sadness at the loss of a colleague and friend, I share the regrets of other contributors to this volume that Paul will not be with us to enjoy the fruits of our labors.

I note that three bound volumes of Paul’s collected works have been assembled by departmental colleagues and that digital copies may be made available to researchers and scholars by contacting the Department of Mechanical and Aerospace Engineering in the University of California, San Diego.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ A list of minor but previously unpublished corrigenda is given below in Appendix A.

² The frequent characterization of this partial equilibrium as a condition of vanishing reaction rate is more appropriately stated as a vanishing of reaction affinity, which tends to zero with the reciprocal of large kinetic constant representing large conductance.