The arbitrary dynamic behavior of open chemical reaction systems

Abstract

We show that if the kinetic equations describing a set of chemical reactions occurring in a one-phase closed system are only required to obey a very general set of postulates (mass conserved, concentrations nonnegative, vector fields which are continuous with continuous derivatives, existence of equilibrium, stability of equilibrium, existence of potential functions which are extremal at equilibrium, detailed balance, law of definite proportions, and a dissipation inequality equivalent to the second law of thermodynamics), then when coupled to input and output flows the kinetic equations are compatible with any local dynamical behavior consistent with the dimension of the chemical state space. From this one can draw one of two conclusions: either open chemical systems are capable of exhibiting any behavior or that there exist additional restrictions on the types of equations that can be used to describe chemical reaction systems.