Application of Haldane's statistical correlation theory in classical systems

TL;DR

This work extends Haldane's statistical correlation framework by introducing nonlinearity through an exponent in the correlation term, revealing a direct link between indistinguishability and the CFES constraint used in classical intermediate statistics. By applying the nonlinear theory to both self-correlating and distinguishable classical systems, the author derives a CFES-equivalent distribution from a quasi-classical MaxEnt approach and shows that MB, FD, and BE statistics arise as limiting cases. A general power-series nonlinearity further expands the landscape of possible intermediate statistics, enabling a tunable family of models via coefficients $b_l$. The study provides a conceptual bridge between indistinguishability and correlation in classical systems and suggests practical uses in enhanced sampling methods for molecular dynamics and related classical contexts.

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.