Thermostatistic properties of the relativistic <Emphasis Type="Italic">q</Emphasis>-deformed ideal Fermi gas at high temperature

The q-deformed Fermi-Dirac distribution is used to study the high-temperature (T > T _F) behavior of a relativistic q-deformed ideal Fermi gas. The effects of the q-deformation and relativity on the properties of the system are discussed, and then, the example of the neutrinos near the surface of the earth is used to calculate approximately. It shows that the q-deformation increases the total energy but decreases the chemical potential and heat capacity, whereas mc ²/?_F0 increases the chemical potential and total energy but decreases the heat capacity (?_F0 is the Fermi energy of ultrarelativistic undeformed Fermi gas). The larger the deformation parameter q and the value of mc ²/?_F0 are, the more remarkable the effects of them on the thermostatistic properties will be. However, the effects of both q-deformation and relativity become weak with increasing temperature. When the temperature, T → ∞ the thermostatistic properties of the system are reduced to those of ordinary Boltzmann gases and independent of q and relativity effect completely, which implies that the q-deformation is a pure quantum effect.