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Power-law distributions and fluctuation-dissipation relation in the stochastic dynamics of two-variable Langevin equations

“…These distributions have been noted prevalently in, for example, glasses [1,2], disordered media [3][4][5], folding of proteins [6], single-molecule conformational dynamics [7,8], trapped ion reactions [9], chemical kinetics, and biological and ecological population dynamics [10,11], reaction-diffusion processes [12], chemical reactions [13], combustion processes [14], gene expressions [15], cell reproductions [16], complex cellular networks [17], small organic molecules [18], astrophysical and space plasmas [19] etc. The typical forms of such power-law distributions which have attracted great attention include the κ-distributions or the generalized Lorentzian distributions in the solar wind and space plasmas [19][20][21][22][23][24], the q-distributions in complex systems within nonextensive statistical mechanics [25,26], and those α-distributions noted in physics, chemistry and elsewhere like P(E) ~ E −α with an index α >0 [9,12,13,18,20,27].…”

Stochastic resonance at nonequilibrium phase transitions

“…Such fluctuations with a 1/f power spectrum were observed experimentally at nonequilibrium phase transitions in thermophysical systems: boiling crisis on a wire heater [7,8], explosive boiling-up of superheated liquid jets [9], ultrasonic cavitations [10], combustion [11], and electric discharge [12].…”

Power law behavior in chemical reactions

“…Investigation of power law behavior in combustion, 15 electrochemical noise and corrosion reactions may also shed light on the underlying physics of these processes. By varying sample size and reactant concentration, parameter tuning is possible that would not be as realizable in the study of avalanche behavior in superconductors, earthquakes or rice piles, for example.…”