Extremal dynamics: A unifying physical explanation of fractals, 1/<i>f</i> noise, and activated processes

Abstract

The properties of physical systems whose observable properties depend upon random exceedances of critical parameters are quantitatively examined. Using extreme value theory, the dynamical behavior of this broad class of systems is derived. This class of systems can exhibit two characteristic signatures: generalized activation when far from equilibrium and noise with a characteristic power spectrum (including 1/f ) when in quasiequilibrium. Fractal structures can also arise from these systems. It is thus demonstrated that generalized activation, noise, and fractals, in some cases, are simply different manifestations of a single common dynamical principle, which is termed ‘‘extremal dynamics.’’ Examples of physical processes governed by extremal dynamics are discussed, including data loss of nonvolatile memories and dielectric breakdown.