Application of Haldane's statistical correlation theory in classical systems

TL;DR

This paper extends Haldane's statistical correlation theory by incorporating non-linearity, enabling classical systems to exhibit intermediate statistics similar to quantum fractional exclusion statistics.

Contribution

It introduces a modified, non-linear correlation theory that links classical and quantum intermediate statistics through a classical derivation.

Findings

Derived a quasi-classical intermediate statistics model.

Showed equivalence to classical fractional exclusion statistics.

Proposed an extended non-linear correlation model.

Abstract

This letter investigates the application of Haldane's statistical correlation theory in classical systems. A modified statistical correlation theory has been proposed by including non-linearity in the form of an exponent into the original theory of Haldane. The dependence of the statistical correlation on indistinguishability is highlighted. Using this modified theory, a quasi-classical derivation of intermediate statistics is shown where indistinguishability can be introduced into distinguishable systems in the form of a statistical correlation. The final result is equivalent to the classical fractional exclusion statistics (CFES), which was derived earlier using a purely classical route. An extended non-linear correlation model based on power series expansion is also proposed, which can produce various intermediate statistical models.