Nonextensive and extensive thermostatistic properties of Fermi systems trapped in different external potentials

The thermostatistic properties of a q-generalized Fermi system trapped in a generic power-law potential are studied, based on the generalized statistic distribution derived from the Tsallis entropy. The total number of particles, the total energy, and the heat capacity at constant volume of the system are derived. The thermostatistic characteristics of the system are discussed in detail. It is found that the thermostatistic properties of such a system depend closely on parameter q, dimensional number of the space, kinetic characteristics of particles and shapes of the external potential, and the external potential has a great influence on the thermostatistie properties of the system. Moreover, it is shown that the results obtained here are very general and can be used to unify the description of the nonextensive and extensive thermostatistie properties of a class of Fermi systems trapped in different external potentials so that the important conclusions of many typical Fermi systems in the literature may be directly derived from the present paper.

Thermostatistic Properties of the Relativistic q-Deformed Ideal Fermi Gas at High Temperature

The q-deformed Fermi-Dirac distribution is used to study the high-temperature（T TF） ∨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 ε F0increases the chemical potential and total energy but decreases the heat capacity（ ε F0is the Fermi energy of ultrarelativistic undeformed Fermi gas） . The larger the deformation parameter q and the value of mc 2 ε F0are,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.