Nonadditive entropy and nonextensive statistical mechanics - Some central concepts and recent applications

Abstract

We briefly review central concepts concerning nonextensive statistical mechanics, based on the nonadditive entropy $S_q=k\frac{1-{\sum }_i{p}_i^q}{q-1}(q\in \mathcal{R};S_1=-k{\sum }_i{p}_i\ln p_i)$. Among others, we focus on possible realizations of the $q$-generalized Central Limit Theorem, including at the edge of chaos of the logistic map, and for quasi-stationary states of many-body long-range-interacting Hamiltonian systems.

15 pages, 9 figs., to appear in Journal of Physics: Conf.Series (IOP, 2010)

References in corpus (12)

• Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
• Power-Law Distributions for a Trapped Ion Interacting with a Classical Buffer Gas
• Analysis of Self-Organized Criticality in the Olami-Feder-Christensen model and in real earthquakes
• Defect turbulence and generalized statistical mechanics
• Central limit behavior of deterministic dynamical systems
• Numerical indications of a q-generalised central limit theorem
• On the diffusive anomalies in a long-range Hamiltonian system
• Power-law statistics and stellar rotational velocities in the Pleiades
• A note on q-Gaussians and non-Gaussians in statistical mechanics
• Analysis of self-organized criticality in Ehrenfest's dog-flea model
• Anomalous diffusion in silo drainage
• On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

Cited by in corpus (18)

• Analysis of return distributions in the coherent noise model
• Note on a q-modified central limit theorem
• Reply to Comment on "Towards a large deviation theory for strongly correlated systems"
• Tsallis information dimension of complex networks
• Probability densities for the sums of iterates of the sine-circle map in the vicinity of the quasi-periodic edge of chaos
• Time--Evolving Statistics of Chaotic Orbits of Conservative Maps in the Context of the Central Limit Theorem
• Generalized Huberman-Rudnick scaling law and robustness of $q$-Gaussian probability distributions
• Weak chaos detection in the Fermi-Pasta-Ulam-$\alpha$ system using $q$-Gaussian statistics
• Self organized criticality in an improved Olami-Feder-Christensen model
• Complex statistics in Hamiltonian barred galaxy models
• Return distributions in dog-flea model revisited
• Inter-occurrence times and universal laws in finance, earthquakes and genomes
• Möbius transforms, cycles and q-triplets in statistical mechanics
• Specific heat and entropy of $N$-body nonextensive systems
• Long memory constitutes a unified mesoscopic mechanism consistent with nonextensive statistical mechanics
• First passage time for subdiffusion: The nonextensive entropy approach versus the fractional model
• The entropy in finite $N$-unit nonextensive systems: the ordinary average and $q$-average
• Matrix approach to generalized ensemble theory for nonequilibrium discrete systems