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arXiv 1107.5231cond-mat.stat-mechphysics.flu-dyn
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作为准平衡态统计量的超统计量：应用于充分发展的turbulence

Superstatistics as the statistics of quasi-equilibrium states: Application to fully developed turbulence

Mohammad Mehrafarin

备注：
To appear in Phys. Rev. E (2011)
发表信息：
Phys. Rev. E 84 (2011) 022102
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摘要：

在非平衡态中，电流是由不可逆过程产生的，该过程将系统带到平衡态，在平衡态中电流消失。我们证明，在一般情况下，一个超统计出现时，系统放松到（静态）准平衡态，而不是只有\textit{mean}电流消失，因为波动。特别是，我们表明，目前与高斯白噪声系统的一个独特的类准平衡态，其中的超统计与Tsallis护送$q$ -分布相吻合。以充分发展的湍流为例，解析地推导出了速度结构函数的幂律谱，修正了对数正态模型中高阶矩递减和Novikov不等式的缺点，得到了与实验数据吻合较好的指数.

英文摘要：

In non-equilibrium states, currents are produced by irreversible processes that take a system toward the equilibrium state, where the current vanishes. We demonstrate, in a general setting, that a superstatistics arises when the system relaxes to a (stationary) quasi-equilibrium state instead, where only the \textit{mean} current vanishes because of fluctuations. In particular, we show that a current with Gaussian white noise takes the system to a unique class of quasi-equilibrium states, where the superstatistics coincides with Tsallis escort $q$-distributions. Considering the fully developed turbulence as an example of such quasi-equilibrium states, we analytically deduce the power-law spectrum of the velocity structure functions, yielding a correction to the log-normal model which removes its shortcomings with regard to the decreasing higher order moments and the Novikov inequality, and obtain exponents that agree well with the experimental data.

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