2025/10/28 by Jae Wan Shim, Shim, Jae Wan
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2510.26821
openalex publication_date 2025/10/28 · openalex created_date 2025/11/05 · openalex updated_date 2026/07/28
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 and a heuristic scaling law, visualised as a contour plot, that together indicate when finite-size effects remain detectable.