When Normality Tests Detect Equilibrium Distributions of Finite N-Body Systems
Abstract
The particle number can be used as a quantitative gauge of non-Gaussianity. This idea extends to systems that are not literally finite by assigning them a notional that captures the same deviation. For an ideal gas with insufficiently large for the thermodynamic limit, the velocity distribution that maximises Havrda-Charv\'at entropy departs markedly from the Maxwell--Boltzmann (Gaussian) form obtained in that limit. We explore how five standard normality tests -- Kolmogorov-Smirnov, Anderson-Darling, Cram\'er--von Mises, Jarque-Bera and Shapiro-Wilk -- respond to samples drawn from this finite- equilibrium distribution. A large-scale Monte Carlo study maps the tests' statistical power across system size and sample size , providing practical reference tables and a heuristic scaling law, visualised as a contour plot, that together indicate when finite-size effects remain detectable.
Keywords
Cite
@article{arxiv.2510.26821,
title = {When Normality Tests Detect Equilibrium Distributions of Finite N-Body Systems},
author = {Jae Wan Shim},
journal= {arXiv preprint arXiv:2510.26821},
year = {2026}
}