Nonextensive statistical mechanics and complex scale-free networks

Nonextensive statistical mechanics and complex scale-free networks

‘aging’ scaling property typical of glassy dynamics when σ → 0. 4) A progression from normal diffusiveness to subdiffusive behavior and finally to a stop in the growth of the mean square displacement as demonstrated by the use of a repeated-cell map. (see Fig. 3) The existence of this analogy is perhaps not accidental since the limit of vanishing noise amplitude σ → 0 involves loss of ergodicity.

Nonextensive statistical mechanics and economics

Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous success in describing, among others, the particular stationary state corresponding to thermal equilibrium. There are, however, vast classes of complex systems...

Duality in nonextensive statistical mechanics.

We revisit recent derivations of kinetic equations based on Tsallis' entropy concept. The method of kinetic functions is introduced as a standard tool for extensions of classical kinetic equations in the framework of Tsallis' statistical mechanics. Our analysis of the Boltzmann equation demonstrates a remarkable relation between thermodynamics and kinetics caused by the deformation of macroscop...

Introduction to Nonextensive Statistical Mechanics

Nonextensive statistical mechanics for hybrid learning of neural networks

This paper introduces a new hybrid approach for learning systems that builds on the theory of nonextensive statistical mechanics. The proposed learning scheme uses only the sign of the gradient, and combines adaptive stepsize local searches with global search steps that make use of an annealing schedule inspired from nonextensive statistics, as proposed by Tsallis. The performance of the hybrid...