Roy Projesh Kumar
The Institute of Mathematical Sciences, 4th Cross Road, C.I.T. Campus, Taramani, Chennai 600113, Tamil Nadu, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, Maharashtra, India.
Phys Rev E. 2022 Jul;106(1-1):014141. doi: 10.1103/PhysRevE.106.014141.
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.
在分数排斥统计的几种模型中，人们推测泡利原理可能被违反，并且这已成功应用于多个量子系统。本文利用最大熵方法研究了排斥统计的一种经典替代方法。玻色 - 爱因斯坦统计与麦克斯韦 - 玻尔兹曼统计之间的差异可以通过一个可分离的量来理解，即不可区分程度。从通常的麦克斯韦 - 玻尔兹曼微观状态计数公式出发，利用拉格朗日乘数法引入与不可区分程度相关的特殊限制，以推导在NVE条件下平衡时的概率分布函数。结果发现，所得的概率分布函数在参数的允许范围内产生正实值。对于稀薄系统，概率分布函数介于费米 - 狄拉克统计和玻色 - 爱因斯坦统计之间，并遵循排斥原理。研究了这种新型统计模型各种变量的性质，并讨论了其在经典热力学中的可能应用。
