Reaction Kinetics Path Based on Entropy Production Rate and Its Relevance to Low-Dimensional Manifolds

Abstract

The equation that approximately traces the trajectory in the concentration phase space of chemical kinetics is derived based on the rate of entropy production. The equation coincides with the true chemical kinetics equation to first order in a variable that characterizes the degree of quasi-equilibrium for each reaction, and the equation approximates the trajectory along at least final part of one-dimensional (1-D) manifold of true chemical kinetics that reaches equilibrium in concentration phase space. Besides the 1-D manifold, each higher dimensional manifold of the trajectories given by the equation is an approximation to that of true chemical kinetics when the contour of the entropy production rate in the concentration phase space is not highly distorted, because the Jacobian and its eigenvectors for the equation are exactly the same as those of true chemical kinetics at equilibrium; however, the path or trajectory itself is not necessarily an approximation to that of true chemical kinetics in manifolds higher than 1-D. The equation is for the path of steepest descent that sufficiently accounts for the constraints inherent in chemical kinetics such as element conservation, whereas the simple steepest-descent-path formulation whose Jacobian is the Hessian of the entropy production rate cannot even approximately reproduce any part of the 1-D manifold of true chemical kinetics except for the special case where the eigenvector of the Hessian is nearly identical to that of the Jacobian of chemical kinetics.

Keywords

• entropy production rate
• chemically reacting systems
• quasi-equilibrium
• low-dimensional manifolds
• element conservation
• steepest descent
• Jacobian
• eigenvectors
• Hessian
• trajectory