Stochastic aspects, nonequilibrium

Finally, neither the effect of external noise, which affects nonequilibrium transitions in chemical and biological systems (Lefever, 1981 Horsthemke Lefever, 1984 Lefever Turner, 1986), nor the stochastic aspects of these transitions (Nicolis, Baras Malek-Mansour, 1984) are considered - with the exception of the glycolytic system (chapter 2). Such a simplification, justified in the first approximation by the absence of systematic noise in the biological systems considered, permits us to avoid complicating from the outset the analysis of systems whose kinetics is already complex. 

Nicolis, G., F. Baras M. Malek-Mansour. 1984. Stochastic aspects of nonequiUbrium transitions in chemical systems. In Nonequilibrium Dynamics of Chemical Systems. A. Pacault C. Vidal, eds. Springer, Berlin, pp. 184-99. 

Stochastic Aspects of Nonequilibrium Transitions in Chemical Systems... 

Stochastic Aspects of Nonequilibrium Transitions in Chemical Systems (plenary lecture). By G. Nicolis, F. Baras, and M. Malek Mansour (With 8 Figures). .. 184... 

Although the collision and transition state theories represent two important methods of attacking the theoretical calculation of reaction rates, they are not the only approaches available. Alternative methods include theories based on nonequilibrium statistical mechanics, stochastic theories, and Monte Carlo simulations of chemical dynamics. Consult the texts by Johnson (62), Laidler (60), and Benson (59) and the review by Wayne (63) for a further introduction to the theoretical aspects of reaction kinetics. 

This observation is fundamental, reveling the fact that the characteristic energies of the Fokker-Planck equation are reactive energies, and in the final, nonequilibrium energies. This aspect is directly correlated with the nonequilibrium character specific for the Fokker-Planck equation while modeling open systems (driven by drift diffusion and factors, stochastic noise, etc.). Moreover, if the analytical solution of the eigen-values for the Schrodinger equation with the potential ) is considered, the consecrated expression is obtained ... 

In this chapter, we have discussed three important aspects of thermodynamics in the presence of flow. By considering different points of view ranging from kinetic and stochastic theories to thermod5mamic theories at mesoscopic and macroscopic levels, we addressed the effects of flow on transport coefficients like diffusion and viscosity, constitutive relations and equations of state. In particular, we focused on how some of these effects may be derived from the framework of mesoscopic nonequilibrium thermod5mamics. 

Space and time-correlation functions of macrovariables around nonequilibrium steady states have recently been calculated from nonequilibrium statistical mechanics [2]. Despite this progress, fluctuation theory for nonequilibrium states remains based, in its essential aspects, on stochastic theory. Specifically, it is assumed that one can define an appropriate set of discrete variables... 

Among various aspects of nonequilibrium phenomena the problem of transient behaviour is one of the most interesting ones. In particular, the relaxation from the unstable state was the subject of many studies Cl]. Recent experiments C23 show that stochastic effects may be very important in explaining irreproducibility of results for some nonlinear chemical systems. 

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