When Normality Tests Detect Equilibrium Distributions of Finite N-Body Systems

2025/10/28 by Shim, Jae Wan
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2510.26821

Abstract

The particle number N 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 N that captures the same deviation. For an ideal gas with N insufficiently large for the thermodynamic limit, the velocity distribution that maximises Havrda-Charvát entropy departs markedly from the Maxwell-Boltzmann (Gaussian) form obtained in that limit. We explore how five standard normality tests-Kolmogorov-Smirnov, Anderson-Darling, Cramér-von Mises, Jarque-Bera and Shapiro-Wilk-respond to samples drawn from this finite-N equilibrium distribution. A large-scale Monte-Carlo study maps the tests' statistical power across system size N and sample size n, providing practical reference tables for deciding when finite-size effects remain detectable.

Citations

• A Test for Normality of Observations and Regression Residuals
• An analysis of variance test for normality (complete samples)

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