论文标题
非平衡统计力学的框架。 ii。粗粒
A framework of nonequilibrium statistical mechanics. II. Coarse-graining
论文作者
论文摘要
对于给定的热力学系统以及给定的粗粒状状态变量的选择，对强力组成定律的了解是任何非平衡建模的基础。在本系列的第一篇论文中，我们确定了如何通过经典波动 - 散落定理（FDT）的概括，构造定律的结构与状态变量波动的分布直接相关。当这些波动可以用扩散过程表示，人们可能会使用绿色kubo型粗粒度方案来查找本构定律。在本文中，我们提出了一种粗糙的方法，该方法是在通过普通马尔可夫过程描述波动时有效的，其中包括扩散作为一种特殊情况。我们通过数值计算简单化学反应$ a \ rightleftarrows b $的本构定律来证明该方法的成功。此外，我们表明，任何类似绿色的kubo样方案都找不到一致的本构法。
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 $A \rightleftarrows B$. Furthermore, we show that one cannot find a consistent constitutive law by any Green-Kubo-like scheme.
