FLUCTUATION DYNAMICS, THERMODYNAMIC ANALOGIES AND ERGODIC BEHAVIOR FOR NONEQUILIBRIUM-INDEPENDENT RATE-PROCESSES WITH DYNAMICAL DISORDER

The stochastic properties of the sojourn times attached to a Markov pr ocess in continuous time and with a finite number of states are descri bed by using a statistical ensemble approach. This approach is applied for investigating the large time behavior of independent rate process es with dynamical disorder. The large time behavior of the system is d escribed in terms of an effective transport operator which can be expr essed as a static average with respect to the stochastic properties of the sojourn times. The method is illustrated by the generalization of the Van den Broeck approach to the generalized Taylor diffusion. Expl icit formulas for the effective transport coefficients and for the flu ctuations of the concentration fields are derived. The results are use d for extending the non-equilibrium generalized thermodynamic formalis ms suggested by Keizer and by Ross, Hunt and Hunt to systems with dyna mical disorder. It is shown that the logarithm of the probability dens ity functional of concentration fluctuations is a Lyapunov functional of the effective transport equation. This Lyapunov functional plays th e role of a generalized nonequilibrium thermodynamic potential which m ay serve as a basis for a thermodynamic description of the average beh avior of the system. The existence and stability of a steady state can be expressed as an extremum condition for the Lyapunov functional. Fo r Taylor diffusion in an external electric field different from zero t he generalized potential has a structure similar to the Helmholtz free energy rather than to the entropy. A generalized chemical potential i s derived as the functional derivative of the Lyapunov functional with respect to the concentration field; the gradient of this generalized chemical potential is the driving force which determines the structure of the effective transport equation.