A Fermat-like Principle for Chemical Reactions in Heterogeneous Systems

Abstract

We formulate a variational principle of Fermat type for chemical kinetics in heterogeneous reacting systems. The principle is consistent with the notion of ‘intrinsic reaction coordinate’ (IRC), the idea of ‘chemical resistance’ (CR) and the second law of thermodynamics. The Lagrangian formalism applies a nonlinear functional of entropy production that follows from classical (single-phase) nonequilibrium thermodynamics of chemically reacting systems or its extension for multiphase systems involving interface reactions and transports. For a chemical flux, a “law of bending” is found which implies that — by minimizing the total resistance — the chemical ray spanned between two given points takes the shape assuring its relatively large part in a region of lower chemical resistivity (a ‘rarer’ region of the medium). In effect, the chemical flux bends into the direction that ensures its shape consistent with the longest residence of the chemical complex in regions of lower resistivity. The dynamic programming method quantifies the “chemical rays” and related wavefronts along the reaction coordinate.