Irreversible random transition theory as applied to rate processes in condensed media: Transient effects of constrained configuration rearrangements in complex systems

A theory of irreversible random transitions has been applied to rate processes coupled to configurational rearrangements of non-equilibrium complex systems. The rearrangements are discussed in terms of three main requirements imposed by the complexity of the object, i.e. the dynamic behavior of various degrees of freedom, constraints arising due to their interactions, and the hierarchy of configurational substates. The simplest possible model that embodies these three principles suggests unusual time behavior of the diffusion coefficient for the hierarchically constrained motion along the reaction coordinate. This determines the time evolution of observables, in particular the relaxation of the reaction barrier and the temperature dependence of the relaxation rate. The approximate analytical results following from our theoretical analysis are shown to be in qualitative agreement with experimental data obtained for proteins and allow theoretical predictions available for further experimental testing.