Thermostatistics of \mu-deformed analog of Bose gas model

TL;DR

This paper introduces a -deformed Bose gas model, developing a new -calculus to analyze its thermodynamics, including virial expansion, critical temperature, and thermodynamic functions, highlighting unique features of the model.

Contribution

The paper develops the -calculus and applies it to derive thermodynamic properties of the -deformed Bose gas, extending previous models with a new deformation parameter.

Findings

Derived virial coefficients as functions of 

Calculated -dependent critical temperature T_c^()

Analyzed thermodynamic functions at high and low temperatures

Abstract

For the recently introduced \mu-deformed analog of Bose gas model (\mu-Bose gas model) we study some thermodynamical aspects. Namely, we calculate total number of particles and, from it, the deformed partition function, both involving dependence on the deformation parameter \mu. Such dependence of thermodynamic functions on the \mu-parameter is at the core of modification of Bose gas model and arises through the use of new techniques given by us, the \mu-calculus, an alternative to the well-known q-calculus (Jackson derivative and integral). Necessary elements of \mu-calculus are first presented. Then, for high temperatures we obtain virial expansion of the equation of state and find five first virial coefficients, as functions of \mu. At the other end, for low temperatures the critical temperature of condensation T_c^(\mu) depending on \mu is found and compared with the usual T_c, and with the T_c^(p,q) of earlier studied p,q-Bose gas model. The internal energy, specific heat and the entropy of \mu-Bose gas are also given, both for high and low temperatures. Features peculiar for the \mu-Bose gas model are emphasized.