Generalized thermodynamics ofq-deformed bosons and fermions

Abstract

We study the thermostatistics of q-deformed bosons and fermions obeying the symmetric $(q\leftrightarrow q^{-1})$ algebra and show that it can be built on the formalism of q calculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by an appropriate Jackson derivative. In this framework, we derive the most important thermodynamic functions describing the q-boson and q-fermion ideal gases in the thermodynamic limit. We also investigate the semiclassical limit and the low-temperature regime and demonstrate that the nature of the q deformation gives rise to pure quantum statistical effects stronger than undeformed boson and fermion particles.