Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems

Logarithmic oscillations superimposed on the temporal relaxation patterns of complex systems are considered from the standpoint of their hierarchical origin. We propose that a closer examination of experimental data should reveal logarithmic oscillations in systems that are characterized by a hierarchical structure of their dynamical degrees of freedom. On that footing, a new methodology of data analysis is proposed that may prove important for the dynamics of protein folding and of conformational fluctuations in proteins in which the relevant time scales of the dynamical evolution underlying the relaxation kinetics can be deduced from these oscillations.