When Normality Tests Detect Equilibrium Distributions of Finite N-Body Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910004760543232 |
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| author | Shim, Jae Wan |
| author_facet | Shim, Jae Wan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | When Normality Tests Detect Equilibrium Distributions of Finite N-Body Systems Shim, Jae Wan Statistical Mechanics 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. |
| title | When Normality Tests Detect Equilibrium Distributions of Finite N-Body Systems |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2510.26821 |