Information theory deals with measurement and transmission of information through a channel. A fundamental work in this area is the Shannon’s Information Theory (see [2], Chapter 11), which provides many useful tools that are based on measuring information in terms of the complexity of structures needed to encode a given piece of information. Shannon’s theory solves two central problems for cla...

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits q-exponential or power law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele-Shaw flow as simulated by the Lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the trans...

– The porous media equation has been proposed as a phenomenological “nonextensive” generalization of classical diffusion. Here, we show that a very similar equation can be derived, in a systematic manner, for a classical fluid by assuming nonlinear response, i.e. that the diffusive flux depends on gradients of a power of the concentration. The present equation distinguishes from the porous medi...

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...

We present a deformed algebra related to the q-exponential and the q-logarithm functions that emerge from nonextensive statistical mechanics. We also develop a q-derivative (and consistently a q-integral) for which the q-exponential is an eigenfunction. The q-derivative and the q-integral have a dual nature, that is also presented.

We introduce an iterative algorithm for finding a common minimum norm fixed point of a finite family of asymptotically nonextensive nonself mappings. A strong convergence theorem of common element is established in a uniformly smooth and uniformly convex Banach space. Mathematics Subject Classification: 47H09; 47H05

Using the generalized maximum entropy principle based on the nonextensive q entropy, a family of random matrix ensembles is generated. This family unifies previous extensions of random matrix theory (RMT) and gives rise to an orthogonal invariant stable Lévy ensemble with new statistical properties. Some of them are analytically derived.

Combination of the Liouville equation with the q-averaged energy Uq = hHiq leads to a microscopic framework for nonextensive q-thermodynamics. The resulting von Neumann equation is nonlinear: i _ = [H; q]. In spite of its nonlinearity the dynamics is consistent with linear quantum mechanics of pure states. The free energy Fq = Uq TSq is a stability function for the dynamics. This implies that q...

We discuss the basic transport phenomena in gases and plasmas obeying the q-nonextensive velocity distribution (power-law). Analytical expressions for the thermal conductivity (Kq) and viscosity (ηq) are derived by solving the Boltzmann equation in the relaxation-time approximation. The available experimental results to the ratio Kq/ηq constrains the q-parameter on the interval 0.74 ≤ q ≤ 1. In...

Stimulated by the recent debate on the physical relevance and on the predictivity of q-Gaussian formalism, we present specific analytical expressions for the parameters characterizing non-Gaussian distributions, such as the nonextensive parameter q, expressions that we have proposed for different physical systems, an important example being plasmas in the stellar cores.