摘要翻译：
仅从统计力学的主要原理出发，导出了流体中分子布朗粒子路径概率分布的精确维里展开式，它将分布的响应与流体的扰动以及分子与布朗粒子的统计关联联系起来。该展开式表明，(i)这些关联的空间扩展是有限的，(ii)这与分子混沌假说所涉及的高斯分布不一致，(iii)实路径分布具有幂律长尾。这意味着，即使在玻尔兹曼-格拉德气体中，实际的布朗路径也永远不会分离成统计上独立的碎片，而是表现得好像布朗粒子的扩散系数经历了无尺度的低频涨落。
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英文标题：
《Virial expansion of molecular Brownian motion versus tales of
  "statistical independency"》
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作者：
Yuriy E. Kuzovlev
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最新提交年份：
2008
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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：Soft Condensed Matter        软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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英文摘要：
  Basing on main principles of statistical mechanics only, an exact virial expansion for path probability distribution of molecular Brownian particle in a fluid is derived which connects response of the distribution to perturbations of the fluid and statistical correlations of its molecules with Brownian particle. The expansion implies that (i) spatial spread of these correlations is finite, (ii) this is inconsistent with Gaussian distribution involved by the ``molecular chaos'' hypothesis, and (iii) real path distribution possesses power-law long tails. This means that actual Brownian path never can be disjointed into statistically independent fragments, even in the Boltzmann-Grad gas, but behaves as if Brownian particle's diffusivity undergoes scaleless low-frequency fluctuations.
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PDF链接：
https://arxiv.org/pdf/802.0288