Nonextensive Quantum H-Theorem

TL;DR

This paper proves a quantum $H$-theorem incorporating nonextensive effects, demonstrating that quantum distributions extend to $q$-power laws and are consistent with standard quantum statistics in the extensive limit.

Contribution

It introduces a nonextensive quantum $H$-theorem and derives quantum $q$-distribution extensions consistent with quantum statistics.

Findings

Nonextensive parameter $q$ is in [0,2].

Quantum $q$-distributions generalize Fermi-Dirac and Bose-Einstein distributions.

Results recover standard quantum statistics in the extensive limit.

Abstract

A proof of the quantum $H$-theorem taking into account nonextensive effects on the quantum entropy $S^Q_q$ is shown. The positiveness of the time variation of $S^Q_q$ combined with a duality transformation implies that the nonextensive parameter $q$ lies in the interval [0,2]. It is also shown that the equilibrium states are described by quantum $q$-power law extensions of the Fermi-Dirac and Bose-Einstein distributions. Such results reduce to the standard ones in the extensive limit, thereby showing that the nonextensive entropic framework can be harmonized with the quantum distributions contained in the quantum statistics theory.