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

TL;DR

This paper introduces a universal kinetic function for complex systems that unifies various fractal kinetic models, incorporating effects of memory, correlations, and energy landscape variations, with applications in biophysics and biotechnology.

Contribution

It presents a generalized kinetic formalism with two exponents, linking fractal kinetics to stochastic relaxation and nonextensive Tsallis theory, unifying diverse complex system behaviors.

Findings

Derived a universal kinetic function for complex systems.

Linked kinetic exponents to energy landscape variations.

Connected fractal kinetics with Tsallis nonextensive theory.

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.