Fluctuations and transitions at chemical instabilities: The analogy to phase transitions

Abstract

The properties of a reacting system near an instability are investigated and the analogy between transitions in unstable systems and equilibrium phase transitions is developed in detail. The set of macroscopic steady state rate equations plays the role of an equation of state. The bifurcation points of this set are analogous to transition and critical points of equilibrium phase transitions. Hard transitions of unstable systems correspond to first order and soft transitions to second and higher order phase transitions. Critical exponents are defined for those properties of the unstable systems which are singular at the transition points, and relations between these critical exponents are investigated. Critical fluctuations are studied with stochastic analogs of the macroscopic rate equations. Both master and Langevin equations are considered and lead to the following conclusions: When a transition or a critical point is approached (a) the amplitude of fluctuations grows; (b) the lifetime of these fluctuations becomes longer; and (c) the spatial correlation length increases. Our approximations are similar to those made in mean field theories of phase transitions and our results are thus ``classical.'' However the critical exponents are not necessarily numerically identical to the Landau-Ginzburg exponents since they depend on the particular nonlinear system.