Extensive form of equilibrium nonextensive statistics

TL;DR

This paper develops an additive formalism for nonextensive statistical mechanics based on Tsallis entropy, leading to exact quantum distributions that differ from traditional approximations and resemble behaviors of strongly correlated electrons.

Contribution

It introduces a new additive formalism respecting thermodynamic equilibrium for nonextensive systems, providing exact quantum distributions.

Findings

Exact quantum gas distributions differ from factorization approximations.

Fermion distributions exhibit behaviors similar to strongly correlated electrons.

Formalism maintains additive properties with q-deformed quantities.

Abstract

It is argued that the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system having Tsallis entropy. So it should be respected by all exact calculations concerning interacting nonextensive subsystems. Using nonextensive energy satisfying the factorization, we propose an additive formalism of nonextensive statistical mechanics with additive q-deformed physical quantities and exponential distributions. This formalism leads to exact quantum gas distributions different from those given by factorization approximation. The fermion distribution of present work shows similar behaviors to that of strongly correlated electrons.