摘要翻译：
实验表明，在稳态非平衡状态下，宏观系统的局部热力学变量具有长程关联。在以前的文献中，我们提出了非平衡态自由能的Hamilton-Jacobi方程作为非平衡态热力学的基本原理。我们在这里说明了如何从任意输运系数的Hamilton-Jacobi方程导出具有外场和边界层的动力学的两点关联式方程。与脉动流体力学不同，该方法可用于导出任意阶关联式的方程。一般而言，关联函数方程的解是非平凡的，表明长程关联确实是非平衡系统的一个共同特征。最后，我们根据输运系数的性质建立了判定局部热力学变量是正相关还是负相关的判据。
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英文标题：
《On the long range correlations of thermodynamic systems out of
  equilibrium》
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作者：
L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim
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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：
  Experiments show that macroscopic systems in a stationary nonequilibrium state exhibit long range correlations of the local thermodynamic variables. In previous papers we proposed a Hamilton-Jacobi equation for the nonequilibrium free energy as a basic principle of nonequilibrium thermodynamics. We show here how an equation for the two point correlations can be derived from the Hamilton-Jacobi equation for arbitrary transport coefficients for dynamics with both external fields and boundary reservoirs. In contrast with fluctuating hydrodynamics, this approach can be used to derive equations for correlations of any order. Generically, the solutions of the equation for the correlation functions are non-trivial and show that long range correlations are indeed a common feature of nonequilibrium systems. Finally, we establish a criterion to determine whether the local thermodynamic variables are positively or negatively correlated in terms of properties of the transport coefficients.
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PDF链接：
https://arxiv.org/pdf/705.2996