Generalization of fluctuation-dissipation relationships

It was demonstrated that flicker-noise spectroscopy (FNS) generalizes the concepts underlying fluctuation-dissipation relationships (FDRs), which are normally used to relate the characteristics of fluctuation dynamics of thermodynamically equilibrium systems with the kinetic parameters describing Maxwellian relaxations. The essence of the FNS approach is to extract information from irregular components of signals (spikes, jumps, kinks in derivatives of various orders) at each space-time level of the hierarchical structure of the system, with the corresponding information-carrying parameters obtained from an analysis of the power spectrum S(f) (f is the frequency) and the difference moments Phi((p))(tau) (tau is the time delay parameter) of various orders p of the measurable dynamic variables. Both the information-carrying functions, S(f) and Phi((p))(tau), not one as in the traditional approach, were treated as FDRs. FDRs for systems in a state close to thermodynamic equilibrium (fluctuations of the electric potential in electron-conductive systems and Levi diffusion) and for strongly non-equilibrium stationary systems (fully developed turbulence and flicker noise) were considered as examples.