Non-extensive entropy of bosonic Fibonacci oscillators

TL;DR

This paper explores the relationship between non-extensive entropy in a two-parameter deformed bosonic gas called Fibonacci oscillators and Tsallis thermostatistics, using Fibonacci calculus to analyze their properties and applications to Bose-Einstein condensation.

Contribution

It introduces a formalism based on Fibonacci calculus for two-parameter deformed bosons and compares their entropy with Tsallis entropy, extending previous one-parameter models.

Findings

Fibonacci calculus effectively describes two-parameter deformed bosons.

The non-extensive entropy functions of these bosons relate to Tsallis entropy.

Recent results on Bose-Einstein condensation are summarized for this generalized gas.

Abstract

We discuss possible connections between the thermostatistical properties of a gas of the two-parameter deformed bosonic particles called Fibonacci oscillators and the properties of the Tsallis thermostatistics. In this framework, we particularly focus on a comparison of the non-extensive entropy functions expressed by these two generalized theories. We also show that the thermostatistics of the two-parameter deformed bosons can be studied by the formalism of Fibonacci calculus, which generalizes the recently proposed formalism by Lavagno and Narayana Swamy of q-calculus for the one-parameter deformed boson gas. As an application, we briefly summarize some of the recent results on the Bose-Einstein condensation phenomenon for the present two-parameter generalized boson gas.