By using the Euler-MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container. The general expressions of the thermodynamic quantities wi...By using the Euler-MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.展开更多
On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy...On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.展开更多
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 o...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.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 10875100)
文摘By using the Euler-MacLaurin formula, this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container. The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed. It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy. It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects, such as the nonextensivity of the system, the anisotropy of the pressure, and so on.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005041)the Natural Science Foundation of Fujian Province, China (Grant No. 2010J05007)+2 种基金the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China (Grant No. 2010-1561)the Basic Science Research Foundation, China (Grant No. JB-SJ1005)the Science Research Fund of Huaqiao University, China (including the support forHuang (Grant No. 11BS207))
文摘On the basis of the entropy of incomplete statistics （IS） and the joint probability factorization condition, two controversial problems existing in IS are investigated： one is what expression of the internal energy is reasonable for a composite system and the other is whether the traditional zeroth law of thermodynamics is suitable for IS. Some new equivalent expressions of the internal energy of a composite system are derived through accurate mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it cannot be proven theoretically. Finally, it is pointed out that the generalized zeroth law of thermodynamics for incomplete nonextensive statistics is unnecessary and the nonextensive assumptions for the composite internal energy will lead to mathematical contradiction.
基金Project supported by the Research Foundation of Ministry of Education, China (Grant No 20050384005)the Science Research Fund, Huaqiao University, China (Grant No 07BS105)
文摘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.
