Nonextensive statistics based on Landsberg-Vedral entropy

TL;DR

This paper develops a formalism for nonextensive statistical mechanics using Landsberg-Vedral entropy, deriving thermodynamic relations and highlighting differences from Tsallis statistics, notably avoiding escort probabilities.

Contribution

It introduces a new nonextensive statistical framework based on Landsberg-Vedral entropy, simplifying the formalism by eliminating the need for escort probabilities.

Findings

Derived the formalism for Landsberg-Vedral entropy-based nonextensive statistics.

Established thermodynamic relations and ensemble averages within this framework.

Showed the formal resemblance to Tsallis statistics under a specific transformation.

Abstract

The general formalism for the nonextensive statistics based on the Landsberg-Vedral entropy was derived. The formula for the first law of thermodynamics and the exact relations of the thermodynamic quantities to their ensemble averages were obtained. It was found that under the transformation $q\to 2-q$ the probabilities of microstates of the nonextensive statistics based on the Landsberg-Vedral entropy formally resemble the corresponding probabilities of the Tsallis statistics with escort probabilities. However, the nonextensive statistics with the Landsberg-Vedral entropy does not require introduction of the escort probabilities and generalized expectation values which are used in this version of the Tsallis statistics.