摘要翻译：
当通过涨落耗散定理把不可逆过程的热力学和随机过程理论联系起来时，必须援引爱因斯坦-玻尔兹曼型公设。对于对流过程，必须考虑水动力波动，速度是一个动力学变量，虽然熵不能直接依赖于速度，但Δs依赖于速度的变化。有些作者在$\delta{2}s$中不包括速度变化，因此不得不引入一个非热力学函数来代替熵，并依赖于速度。乍一看，引入这样一个函数似乎需要对爱因斯坦-玻尔兹曼关系进行推广。我们回顾了为什么没有必要引入这样一个函数的原因，以及为什么没有必要以这种方式推广爱因斯坦-玻尔兹曼关系的原因。然后，我们得到了与非对流情形相比有一些不同的涨落-耗散定理。我们还证明了当包含速度涨落时，$\delta{2}s$是一个Liapunov函数。
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英文标题：
《The Einstein-Boltzmann Relation for Thermodynamic and Hydrodynamic
  Fluctuations》
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作者：
A. J. McKane, F. Vazquez and M. A. Olivares-Robles
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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：Mesoscale and Nanoscale Physics        介观和纳米物理
分类描述：Semiconducting nanostructures: quantum dots, wires, and wells. Single electronics, spintronics, 2d electron gases, quantum Hall effect, nanotubes, graphene, plasmonic nanostructures
半导体纳米结构：量子点、线和阱。单电子学，自旋电子学，二维电子气，量子霍尔效应，纳米管，石墨烯，等离子纳米结构
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英文摘要：
  When making the connection between the thermodynamics of irreversible processes and the theory of stochastic processes through the fluctuation-dissipation theorem, it is necessary to invoke a postulate of the Einstein-Boltzmann type. For convective processes hydrodynamic fluctuations must be included, the velocity is a dynamical variable and although the entropy cannot depend directly on the velocity, $\delta^{2} S$ will depend on velocity variations. Some authors do not include velocity variations in $\delta^{2} S$, and so have to introduce a non-thermodynamic function which replaces the entropy and does depend on the velocity. At first sight, it seems that the introduction of such a function requires a generalisation of the Einstein-Boltzmann relation to be invoked. We review the reason why it is not necessary to introduce such a function, and therefore why there is no need to generalise the Einstein-Boltzmann relation in this way. We then obtain the fluctuation-dissipation theorem which shows some differences as compared with the non-convective case. We also show that $\delta^{2} S$ is a Liapunov function when it includes velocity fluctuations.
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PDF链接：
https://arxiv.org/pdf/710.5743