Abstract For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green–Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction A ⇄ BA\rightleftarrows B. Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green–Kubo-like scheme.

中文翻译：

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非平衡统计力学框架。二、粗粒度

摘要 对于给定的热力学系统和粗粒度状态变量的给定选择，力-通量本构定律的知识是任何非平衡建模的基础。在本系列的第一篇论文中，我们通过对经典波动耗散定理 (FDT) 的推广，确定了本构律的结构如何与状态变量的波动分布直接相关。当这些波动可以用扩散过程表示时，可以使用 Green-Kubo 型粗粒度方案来找到本构规律。在本文中，我们提出了一种粗粒度方法，该方法在通过一般马尔可夫过程描述波动时有效，其中包括作为特殊情况的扩散。