The thermostatistic problems of a q-deformed ideal Fermi gas in any dimensional space and with a general energy spectrum are studied, based on the q-deformed Fermi-Dirac distribution. The effects of the deformation parameter q on the properties of the system are revealed. It is shown that q-deformation results in some novel characteristics different from those of an ordinary system. Besides, it is found that the effects of the q-deformation on the properties of the Fermi systems are very different for different dimensional spaces and different energy spectrums.

The q-deformed Bose–Einstein distribution derived from the q-boson algebra is used to study the low-temperature behavior of an ideal q-deformed Bose gas with relativistic energy spectrum. The effects of q-deformation on the properties relative to Bose–Einstein condensation (BEC) are discussed. It is shown that q-deformation leads to some novel characteristics different from those of an original Bose gas, which include the criteria on the occurrence of BEC, critical temperature and jump of heat capacity at the critical point. The results obtained here provide a unified description for the properties of q-deformed Bose systems from the nonrelativistic case to the ultrarelativistic limit, so that some important conclusions in the literature are included in this paper.

The q-deformed Fermi-Dirac distribution derived from the q-fermion algebra is used to study the thermostatistical properties of a q-deformed Fermi gas trapped in a generic power-law potential, and the effects of q-deformation on the properties of the system are discussed. It is shown that q-deformation leads to some novel characteristics compared with those of an original Fermi system. It is found that the effects of q-deformation display different characteristics in the cases of different kinematic characteristics of particles and different shapes of external potentials. The results obtained here present a unified description for the thermostatistical properties of a class of q-deformed as well as original Fermi systems, so that many important conclusions in the literature are included in this paper.National Science Foundation of Fujian Province, People's Republic of China [Z0512002

Thermodynamic properties of a relativistic Fermi gas in any dimensional space are studied, in which the influence of particle–antiparticle pair production is taken into account. It is shown that relativistic effects cannot be ignored even at very low temperatures for the system with the Compton wavelength of a particle comparable with the average distance between particles. The pair production results in some novel characteristics, which include the asymptotic behavior of the chemical potential and the rapid increase in the heat capacity with temperature in the high temperature regions, etc.