第八种统计分布、涨落及热力学平衡态的稳定性

第八种统计分布、涨落及热力学平衡态的稳定性 The Eighth Statistical Distribution,Fluctuations and Stability of Thermodynamic Equilibrium State 李鹤龄 LI Heling 1 first-author 宁夏大学物理电气信息学院,宁夏,银川,750021 宁夏大学物理电气信息学院,宁夏,银川,750021 College of Physics and Electrical Information, Ningxia University College of Physics and Electrical Information, Ningxia University 由Jaynes最大信息熵原理及拉格朗日乘子法推导出第八种统计分布,通过引入非广延熵常数的方法解决了零系综的困难.理论验证表明:本文推导出的第八种分布（N-E-V分布）不仅适用于小系统,而且适用于大系统.由此分布计算的理想量子系统的热力学量与7种分布相同,但广延量相对涨落却是正比于1的.这不仅可以解释临界现象,也说明热力学平衡态及近平衡定态并不总是稳定的. The eighth statistical distribution is simply derived by Jaynes’ maximum-entropy principle and Lagrange multiplier algorithm. The embarrassment of zero ensemble is solved by introducing a constant of nonextensive entropy. It is demonstrated that the eighth distribution is suitable for not only small systems, but also the large systems. The thermodynamic functions and the relatively fluctuations in the extensive quantities of Bose and Fermi systems are computed by the eighth statistical distribution, and the results of the thermodynamic functions are completely the same as ones in other distributions. But the relatively fluctuations are also in proportion to 1. Critical phenomena can be explained without the difficulty in traditional statistical mechanics. Hence it is demonstrated that the thermodynamic equilibrium states and nearly-equilibrium states are not always stable. 统计力学 热力学公式 统计分布 相对涨落 平衡态不稳定 statistical mechanics thermodynamic formula statistical distribution relative fluctuation unstable equilibrium state O414.2 宁夏回族自治区自然科学基金资助项目（NZ0605） 2008-01-01 2021-04-01 1