TESTS OF THERMODYNAMIC THEORY OF RELATIVE STABILITY IN ONE-VARIABLE SYSTEMS

Schlogl's criterion for equistability of two stable stationary states of an inhomogeneous chemical kinetic system is valid only for single-variable cases dependent along a single spatial coordinate. We test the thermodynamic theory, developed in the preceding article for multivariable systems, in one dimension by comparison with calculations based on the deterministic reaction-diffusion equation for a cubic Schlogl model (single variable). This reaction-diffusion system is equivalent to a coupled multivariable system. The prediction of the thermodynamic theory of equistability approaches Schlogl's result as the length of the system increases. We also test the theory for an optically bistable (ZnSe) system which has been studied experimentally; in this system, temperature is the variable, and there is transport by thermal conduction. Again, we find that the prediction of the multivariable thermodynamic theory approaches the result from the deterministic kinetic equation as the length of the system increases. Further, the single-variable thermodynamic theory of relative stability of homogeneous steady states agrees with experiments and with the prediction of the deterministic equation.