Thermodynamic Potentials and Evolution towards the Stationary State in Open Systems of Far-from-Equilibrium Chemical Reactions: The Affinity Squared Minimum Function

Abstract

The “evolutionary” characteristics of several quadratic functions (based both on the affinities and on the reaction velocities), and of the entropy production per unit time, have been studied for a number of 2-variable open systems of far-from-equilibrium chemical reactions. The first and second order systems were chosen to include: straight line, loop (network), autocatalytic and disproportionate kinetic features. All of the functions examined are closely related in form to the entropy production though they differ qualitatively and quantitatively in the non-linear domain. By a combination of analytical and computational methods one function, called µ, is seen to have the variational properties of a “thermodynamic potential” for all of the systems, relative to their non-equilibrium stationary states. The “homeostatic-like” stability criterion, $\frac{{{\rm{d\mu }}}}{{{\rm{df}}}} \le {\rm{0}}$ is also seen to hold for these systems. The function, a composite property of the system, may Be interpreted as a “kinetically-weighted system-free-energy” quantity, which would tend to be minimized during the evolution, in configuration and in space time, of a constrained biochemical system.