Deterministic and Stochastic Asymptotic Behavior of Nonequilibrium Chemical Systems with Time-Dependent Rate Coefficients

Abstract

We analyze the long time limit of the nonequilibrium solutions of a system of multivariable nonlinear kinetic equations with time-dependent rate coefficients, as achieved, for example, by temporal variation of the temperature. If the characteristic time scale attached to the change of rate coefficients is smaller than the relaxation time to equilibrium, then the system is constrained to evolve away, possibly far, from equilibrium. However, after a sufficiently large time the system forgets its past: in the long run all solutions of the kinetic equations tend toward a special (normal) solution which depends on the previous values of the rate coefficients, but it is independent of the initial state of the system. The normal solution may be very different from the equilibrium solution. The occurrence of this type of time-dependent normal regime for the deterministic kinetic equations is intimately connected to a similar behavior of the stochastic evolution equation of the system. In the long run all solutio...