Generalized Fractal Kinetics in Complex Systems (Application to Biophysics and Biothechnology)

Abstract

We derive a universal function for the kinetics of complex systems. This kinetic function unifies and generalizes previous theoretical attempts to describe what has been called "fractal kinetic".The concentration evolutionary equation is formally similar to the relaxation function obtained in the stochastic theory of relaxation, with two exponents a and n. The first one is due to memory effects and short-range correlations and the second one finds its origin in the long-range correlations and geometrical frustrations which give rise to ageing behavior. These effects can be formally handled by introducing adequate probability distributions for the rate coefficient. We show that the distribution of rate coefficients is the consequence of local variations of the free energy (energy landscape) appearing in the exponent of the Arrhenius formula. We discuss briefly the relation of the (n,a) kinetic formalism with the Tsallis theory of nonextensive systems.