4,377 research outputs found
Generalized statistical mechanics for superstatistical systems
Mesoscopic systems in a slowly fluctuating environment are often well
described by superstatistical models. We develop a generalized statistical
mechanics formalism for superstatistical systems, by mapping the
superstatistical complex system onto a system of ordinary statistical mechanics
with modified energy levels. We also briefly review recent examples of
applications of the superstatistics concept for three very different subject
areas, namely train delay statistics, turbulent tracer dynamics, and cancer
survival statistics.Comment: 9 pages, 5 figure
Superstatistical Brownian motion
As a main example for the superstatistics approach, we study a Brownian
particle moving in a d-dimensional inhomogeneous environment with macroscopic
temperature fluctuations. We discuss the average occupation time of the
particle in spatial cells with a given temperature. The Fokker-Planck equation
for this problem becomes a stochastic partial differential equation. We
illustrate our results using experimentally measured time series from
hydrodynamic turbulence.Comment: 11 pages, 2 figures. To appear in the proceedings of the
international workshop `Complexity and Nonextensivity', Kyoto, 14-18 March
2005 (Progr. Theor. Phys. Suppl.
Superstatistics: Theory and Applications
Superstatistics is a superposition of two different statistics relevant for
driven nonequilibrium systems with a stationary state and intensive parameter
fluctuations. It contains Tsallis statistics as a special case. After briefly
summarizing some of the theoretical aspects, we describe recent applications of
this concept to three different physical problems, namely a) fully developed
hydrodynamic turbulence b) pattern formation in thermal convection states and
c) the statistics of cosmic rays.Comment: 16 pages, 5 figures. Submitted to Continuum Mechanics and
Thermodynamics as a contribution to the topical issue on nonextensive
statistical mechanic
Dynamical foundations of nonextensive statistical mechanics
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.Comment: 7 pages, 1 figur
Complexity of chaotic fields and standard model parameters
In order to understand the parameters of the standard model of electroweak
and strong interactions (coupling constants, masses, mixing angles) one needs
to embed the standard model into some larger theory that accounts for the
observed values. This means some additional sector is needed that fixes and
stabilizes the values of the fundamental constants of nature. In these lecture
notes we describe in nontechnical terms how such a sector can be constructed.
Our additional sector is based on rapidly fluctuating scalar fields that,
although completely deterministic, evolve in the strongest possible chaotic way
and exhibit complex behaviour. These chaotic fields generate potentials for
moduli fields, which ultimately fix the fundamental parameters. The chaotic
dynamics can be physically interpreted in terms of vacuum fluctuations. These
vacuum fluctuations are different from those of QED or QCD but coupled with the
same moduli fields as QED and QCD are. The vacuum energy generated by the
chaotic fields underlies the currently observed dark energy of the universe.
Our theory correctly predicts the numerical values of the electroweak and
strong coupling constants using a simple principle, the minimization of vacuum
energy. Implementing some additional discrete symmetry assumptions one also
obtains predictions for fermion masses, as well as a Higgs mass prediction of
154 GeV.Comment: 27 pages, 7 figures. Invited lectures given at the Erice summer
school `The Logic of Nature, Complexity and New Physics: From Quark-Gluon
Plasma to Superstrings, Quantum Gravity and Beyond' (Erice, 29 Aug.-7. Sept.
2006
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