The q-deformed Fermi-Dirac distribution is used to study the high-temperature F ( ) T T ∨ 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 2 F0 mc ε increases the chemical potential and total energy but decreases the heat capacity ( F0 ε is the Fermi energy of ultrarelativistic undeformed Fermi gas). The larger the deformation parameter q and the value of 2 F0 mc ε 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.
The analytical expressions of internal energy, chemical potential and heat capacity of the little parameter r for a weakly interacting Fermi gas in weak magnetic field are derived by using “pseudopotential" method and ensemble theory. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas in weak magnetic field at both high and low temperatures are given. The effects of magnetic field and interparticle interactions on the thermodynamic properties are discussed. The difference in the effects of magnetic trap and three-dimensional harmonic trap on the properties of the system and their reasons are analyzed.
When the orbital motion and the spin motion of particles were considered simultaneously, the thermodynamic potential function of a weakly interacting Fermi gas in a weak magnetic field was derived using the thermodynamics method. Based on the derived expression, the analytical expressions of energy, heat capacity, chemical potential, susceptibility and stability conditions of the system were given, and the effects of the interparticle interactions as well as the magnetic field on the properties of the system were analyzed. It was shown that the magnetic field always causes energy and stability to decrease, while the chemical potential of the system to increase. The repulsive (attractive) interactions always increase (decrease) energy and stability, but decrease (increase) the chemical potential and paramagnetism. The repulsive (attractive) interactions decrease (increase) heat capacity of the system at high temperatures but increase (decrease) it at low temperatures.Fermi gas, magnetic field, interaction, statistical property
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