Archive for Rational Mechanics and Analysis

, Volume 47, Issue 2, pp 81–116

General mass action kinetics


  • F. Horn
    • University of Rochester
    • Rice University
  • R. Jackson
    • University of Rochester
    • Rice University

DOI: 10.1007/BF00251225

Cite this article as:
Horn, F. & Jackson, R. Arch. Rational Mech. Anal. (1972) 47: 81. doi:10.1007/BF00251225


The familiar idea of mass action kinetics is extended to embrace situations more general than chemically reacting mixtures in closed vessels. Thus, for example, many reaction regions connected by convective or diffusive mass transport, such as the cellular aggregates of biological tissue, are drawn into a common mathematical scheme.

The ideas of chemical thermodynamics, such as the algebraic nature of the equilibrium conditions and the decreasing property of the free energy, are also generalized in a natural way, and it is then possible to identify classes of generalized kinetic expressions which ensure consistency with the extended thermodynamic conditions. The principal result of this work shows that there exists a simply identifiable class of kinetic expressions, including the familiar detailed balanced kinetics as a proper subclass, which ensure consistency with the extended thermodynamic conditions. For kinetics of this class, which we call complex balanced kinetics, exotic behavior such as bistability and oscillation is precluded, so the domain of search for kinetic expressions with this type of behavior, which is of considerable biological interest, is greatly narrowed.

It is also shown that the ideas of complex balancing and of detailed balancing are closely related to symmetry under time reversal.

Copyright information

© Springer-Verlag 1972