摘要翻译：
在一个典型的长程相互作用多体经典哈密顿系统HMF模型中，我们给出了中心极限定理(CLT)的分子动力学检验。我们计算了在不同尺寸和能量密度下，沿确定性轨迹在等距时间内的速度之和。我们证明，当系统处于混沌状态时（特别是在热平衡状态下），遍历性得到了本质上的验证，和的Pdfs似乎是高斯的，与标准CLT一致。相反，当系统只有弱混沌（特别是沿长期亚稳态）时，观察到非遍历性（即不一致的系综和时间平均），并出现鲁棒的$q$-高斯吸引子，这与最近证明的CLT的推广一致。
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英文标题：
《Nonergodicity and Central Limit Behavior for Long-range Hamiltonians》
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作者：
A. Pluchino, A. Rapisarda and C. Tsallis
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Nuclear Theory        核理论
分类描述：Nuclear Theory Theory of nuclear structure covering wide area from models of hadron structure to neutron stars. Nuclear equation of states at different external conditions. Theory of nuclear reactions including heavy-ion reactions at low and high energies. It does not include problems of data analysis, physics of nuclear reactors, problems of safety, reactor construction
核理论涵盖从强子结构模型到中子星等广泛领域的核结构理论。不同外部条件下的核状态方程。核反应理论，包括低能和高能的重离子反应。它不包括数据分析问题、核反应堆物理问题、安全问题、反应堆建设问题
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  We present a molecular dynamics test of the Central Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic trajectories for different sizes and energy densities. We show that, when the system is in a chaotic regime (specifically, at thermal equilibrium), ergodicity is essentially verified, and the Pdfs of the sums appear to be Gaussians, consistently with the standard CLT. When the system is, instead, only weakly chaotic (specifically, along longstanding metastable Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time averages) is observed, and robust $q$-Gaussian attractors emerge, consistently with recently proved generalizations of the CLT.
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PDF链接：
https://arxiv.org/pdf/706.4021