Semiclassical statistical mechanics' tools for deformed algebras

TL;DR

This paper develops semiclassical tools like Husimi distributions and Wehrl entropy for deformed algebras using q-deformed coherent states, exploring their temperature dependence and behavior as deformation approaches unity.

Contribution

It introduces new semiclassical distributions and entropy measures based on deformed algebras, extending existing tools with a focus on q-deformation and escort distributions.

Findings

Husimi distributions and Wehrl entropy are explicitly derived for q-deformed coherent states.

The generalized Wehrl entropy with escort distributions is analyzed.

Behavior of these quantities as functions of temperature and deformation parameter is studied.

Abstract

In order to enlarge the present arsenal of semiclassical toools we explicitly obtain here the Husimi distributions and Wehrl entropy within the context of deformed algebras built up on the basis of a new family of q-deformed coherent states, those of Quesne [J. Phys. A 35, 9213 (2002)]. We introduce also a generalization of the Wehrl entropy constructed with escort distributions. The two generalizations are investigated with emphasis on i) their behavior as a function of temperature and ii) the results obtained when the deformation-parameter tends to unity.