论文标题
符合分数排除原理的经典系统统计模型的推导
Derivation of a statistical model for classical systems obeying fractional exclusion principle
论文作者
论文摘要
违反Pauli原则的行为已在分数排除统计数据的几种模型中被推测，并成功地应用于多个量子系统。在本文中，使用最大熵方法研究了排除统计的经典替代方案。 Bose-Einstein统计数据与Maxwell-Boltzmann统计数据之间的差异是从可分离的数量来理解的，即无法区分的程度。从通常的Maxwell-Boltzmann Microstate计数公式开始，使用Lagrange乘法器纳入了与无法区分性的特殊限制，以在NVE条件下在平衡处得出概率分布函数。发现所产生的概率分布函数在允许的参数范围内生成真实的正值。对于稀释系统，概率分布函数介于费米 - 迪拉克（Fermi-Dirac）和Bose-Einstein统计之间，并遵循排除原理。研究了该新型统计模型的各种变量的性质，并讨论了在经典热力学上的应用。
The violation of the Pauli principle has been surmised in several models of the Fractional Exclusion Statistics and successfully applied to several quantum systems. In this paper, a classical alternative of the exclusion statistics is studied using the maximum entropy methods. The difference between the Bose-Einstein statistics and the Maxwell-Boltzmann statistics is understood in terms of a separable quantity, namely the degree of indistinguishability. Starting from the usual Maxwell-Boltzmann microstate counting formula, a special restriction related to the degree of indistinguishability is incorporated using Lagrange multipliers to derive the probability distribution function at equilibrium under NVE conditions. It is found that the resulting probability distribution function generates real positive values within the permissible range of parameters. For a dilute system, the probability distribution function is intermediate between the Fermi-Dirac and Bose-Einstein statistics and follows the exclusion principle. Properties of various variables of this novel statistical model are studied and possible application to classical thermodynamics is discussed.
