Thermostatistics of deformed bosons and fermions

TL;DR

This paper explores the thermodynamics of q-deformed bosons and fermions using q-calculus, deriving key thermodynamic functions and analyzing ideal gases within this framework.

Contribution

It introduces a formalism for thermostatistics of q-deformed particles using Jackson derivatives and q-integrals, extending traditional thermodynamics.

Findings

Thermodynamics can be formulated with q-calculus replacing ordinary derivatives.

Derived thermodynamic functions for q-boson and q-fermion gases.

Analyzed the behavior of q-deformed gases in the thermodynamic limit.

Abstract

Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of q-calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most important thermodynamic functions and we study the q-boson and q-fermion ideal gas in the thermodynamic limit.