Quantum statistical mechanics for nonextensive systems

Quantum Statistical Mechanics for Nonextensive Systems II

In this paper, the Green function theory of quantum many-particle systems recently presented is reworked within the framework of nonextensive statistical mechanics with a new normalized q-expectation values. This reformulation introduces a renormalization of temperature of the earlier theory and a self-consistency condition. The linear response theory is also presented, along with its two-parti...

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...

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...

Introduction to Nonextensive Statistical Mechanics

Dynamical scenario for nonextensive statistical mechanics

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann-Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions , mixing and ergodicity in Gibbs Γ-space. What are the corresponding hypothesis for nonextensive statistical mechanics? A scenario for ...