Abstract
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.
- Received 13 April 2022
- Accepted 11 July 2022
- Corrected 16 August 2022
DOI:https://doi.org/10.1103/PhysRevE.106.014141
©2022 American Physical Society
Physics Subject Headings (PhySH)
Corrections
16 August 2022
Correction: Equation (8) and a formula appearing directly after contained errors and have been fixed. Related details in the Supplemental Material Sec. SI.IV also were modified and the new file has been uploaded.