摘要翻译：
对于按次扩散连续时间随机游动建模的系统，我们给出了时均可观测量分布的一般公式。对于与热浴耦合的高斯随机游动，我们恢复了遍历性和Boltzmann统计量；对于反常次扩散情形，我们根据L\'Evy的广义中心极限定理构造了弱非遍历统计力学框架。作为一个例子，我们计算了在无偏和均匀偏置的情况下，$\bar{X}$的分布：粒子位置的时间平均值，表明$\bar{X}$与系综平均值$<X>$相比有很大的起伏。
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英文标题：
《Distribution of Time-Averaged Observables for Weak Ergodicity Breaking》
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作者：
Adi Rebenshtok, Eli Barkai
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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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英文摘要：
  We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly non-ergodic statistical mechanical framework is constructed, which is based on L\'evy's generalized central limit theorem. As an example we calculate the distribution of $\bar{X}$: the time average of the position of the particle, for unbiased and uniformly biased particles, and show that $\bar{X}$ exhibits large fluctuations compared with the ensemble average $<X>$.
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PDF链接：
https://arxiv.org/pdf/707.3865