Power-law tails in turbulent magnetic field PDFs arise from intermittent Poisson-distributed shocks convolved with a lognormal core, with tail asymmetry determined by the ratio of fast to slow MHD shocks.
Dynamical foundations of nonextensive statistical mechanics
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abstract
We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which ordinary Langevin equations underly ordinary statistical mechanics to the more general nonextensive case. As a main example, we construct a dynamical model of velocity fluctuations in a turbulent flow, which generates probability densities that very well fit experimentally measured probability densities in Eulerian and Lagrangian turbulence. Our approach provides a dynamical reason why many physical systems with fluctuations in temperature or energy dissipation rate are correctly described by Tsallis statistics.
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The dynamical origin of the magnetic field distributions in compressible turbulence
Power-law tails in turbulent magnetic field PDFs arise from intermittent Poisson-distributed shocks convolved with a lognormal core, with tail asymmetry determined by the ratio of fast to slow MHD shocks.