A class of energy based ensembles in Tsallis statistics

TL;DR

This paper explores a comprehensive classification and unified framework for energy-based ensembles within Tsallis statistics, covering isothermal and adiabatic classes with applications to ideal gas models in various relativistic regimes.

Contribution

It introduces a unified description of eight energy-based ensembles in Tsallis statistics, encompassing both isothermal and adiabatic classes, with formulations in second and third constraint formalisms.

Findings

Unified framework for four isothermal ensembles

Application to classical and relativistic ideal gases

Formulation of four adiabatic ensembles

Abstract

A comprehensive investigation is carried out on the class of energy based ensembles. The eight ensembles are divided into two main classes. In the isothermal class of ensembles the individual members are at the same temperature. A unified framework is evolved to describe the four isothermal ensembles. Such a description is provided both in the second and the third constraint formalisms. The isothermal- isobaric, grandcanonical and the generalized ensembles are illustrated through a study of the classical nonrelativistic and the extreme relativistic ideal gas models. In the adiabatic class of ensembles the individual members of the ensemble have the same value of the heat function and a unified formulation to described all the four ensembles is given. The nonrelativistic and the extreme relativistic ideal gases are studied in the isoenthalpic-isobaric ensemble, the adiabatic ensemble with number fluctuations, and, the adiabatic ensemble with number and particle fluctuations.