Abstract
A stochastic description of chain reactions occurring in disordered systems is suggested by considering a statistical distribution of time-dependent rate coefficients. The possibilities of constructing a thermodynamic formalism for non-equilibrium chain reactions are investigated by testing the validity of the eikonal approximation in the thermodynamic limit. If the fluctuations of the rate coefficient are restricted to a finite range, then for large systems the probability of concentration fluctuations obeys the eikonal scaling condition, which makes possible the development of a nonequilibrium thermodynamic formalism. For an infinite range of variation of the rate coefficient, however, the eikonal scaling does not hold anymore: the probability of concentration fluctuations has a long tail of the negative power-law type and the system displays statistical fractal features. The passage from the stochastic eikonal behavior to the fractal scaling is characterized by a change in the deterministic kinetic equations of the process: in the eikonal regime the effective reaction order with respect to the active intermediate is 1, whereas for fractal scaling it is equal to 2. Due to this change in the effective reaction order for fractal scaling, the reaction is much faster than in the eikonal regime and the explosion threshold may be reached after a finite time interval.
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Paper dedicated to Professor Edward A. Mason.
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Vlad, M.O., Ross, J. A stochastic approach to nonequilibrium chain reactions in disordered systems: Breakdown of eikonal approximation. Int J Thermophys 18, 957–975 (1997). https://doi.org/10.1007/BF02575241
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DOI: https://doi.org/10.1007/BF02575241