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The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In this article we investigate the canonical ensemble in the non-extensive statistical mechanics using a more traditional way, by considering a small system interacting with a large reservoir via short-range forces. The reservoir is characterized by generalized entropy instead of the Boltzmann-Gibbs entropy. Assuming equal probabilities for all available microstates we derive the equations of the non-extensive statistical mechanics. Such a procedure can provide deeper insight into applicability of the non-extensive statistics.
The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to physical
We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functio
We propose a two-parametric non-distributive algebraic structure that follows from $(q,q)$-logarithm and $(q,q)$-exponential functions. Properties of generalized $(q,q)$-operators are analyzed. We also generalize the proposal into a multi-parametric
Noethers calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the free energy
In this work the non-equilibrium density operator approach introduced by Zubarev more than 50 years ago to describe quantum systems at local thermodynamic equilibrium is revisited. This method - which was used to obtain the first Kubo formula of shea