Shim, Jae Wan 2026-02-27T05:00:06Z 2026-02-27T05:00:06Z 2026-02-27 2026-02 0020-7748 https://pubs.kist.re.kr/handle/201004/154384 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 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 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. English Springer When Normality Tests Detect Equilibrium Distributions of Finite N-Body Systems Article 10.1007/s10773-025-06229-6 1 International Journal of Theoretical Physics, v.65, no.3 International Journal of Theoretical Physics 65 3 N scie scopus 001701750000001 Physics, Multidisciplinary Physics Article Entropy Information theory Statistics Power test