Thermodynamic and stochastic theory of reaction-diffusion systems with multiple stationary states

Abstract

The thermodynamic and stochastic theory of chemical systems far from equilibrium is extended to reactions in inhomogeneous system for both single and multiple intermediates, with multiple stationary states coupled with linear diffusion. The theory is applied to the two variable Selkov model coupled with diffusion, in particular to the issue of relative stability of two stable homogeneous stationary states as tested in a possible inhomogeneous experimental configuration. The thermodynamic theory predicts equistability of such states when the excess work from one stationary state to the stable inhomogeneous concentration profile equals the excess work from the other stable stationary state. The predictions of the theory on the conditions for relative stability are consistent with solutions of the deterministic reaction-diffusion equations. In the following article we apply the theory again to the issue of relative stability for single-variable systems, and make comparison with numerical solutions of the reaction-diffusion equations for the Schlögl model, and with experiments on an optically bistable system where the kinetic variable is temperature and the transport mechanism is thermal conduction.