The Path Probability Method
The Path Probability Method
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路径概率法
DOI：
10.1143/ptps.35.1
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发表时间：
1966
影响因子：
--
通讯作者：
R. Kikuchi
中科院分区：
文献类型：
--
作者：
R. Kikuchi
综述了不可逆统计力学的路径概率方法，并将其应用于合作系统的扩散和松弛过程。对作者以前报告的部分内容进行了更正和扩充。在第一部分中，表明不可逆情况可以通过在平衡统计力学中添加空间轴来表述，并且系统在时间上采取的最可能路径是通过最大化路径概率来推导的。指出了两种与热浴的相互作用，并介绍了一种新的活化工艺配方。第二部分讨论了原子在晶体中的扩散，假设了空位机制。利用对激活过程的新解释，Reiss的一维结果得到了证实。导出了一般二元固溶体的扩散系数，并讨论了特殊情况。Reiss引入的扩散活度概念在三维上简化了单组分系统的扩散系数，但对二元系统却没有简化。给出了路径变量公式的简单解释，并指出了叠加近似的隐式使用。第三部分讨论了合作系统的松弛过程。以一维非齐次Ising模型为例。利用原子迁移的空位机制讨论了二元有序-无序体系（50-50组成）。导出了均匀相阶参量的弛豫时间。
The path probability method of irreversible statistical mechanics is reviewed and is applied to diffusion and relaxation processes in cooperative systems. Parts of previous reports by the author are corrected and expanded.In Part I it is shown that the irreversible case can be formulated by adding a space axis to the equilibrium statistical mechanics, and that the most probable path in time taken by the system is derived by maximizing the path probability. Two kinds of interaction with the heat bath are pointed out and a new formulation for the activated process is introduced.In Part II atomic diffusion in crystals, assuming the vacancy mechanism, is discussed. Using the new interpretation of the activation process, Reiss's result for one dimension is confirmed. The diffusion coefficient is derived for a general binary solid solution, and special cases are discussed. The concept of the diffusion activity introduced by Reiss does simplify the diffusion coefficient for a one-component system in three dimension, but not for a binary system. A simple interpretation of the formula for the path variables is presented, and the implicit use of a superposition approximation is pointed out.In Part III relaxation processes of cooperative systems are discussed. An inhomogeneous one-dimensional Ising model is treated as an example. A binary order-disorder system (of 50-50 composition) is discussed using the vacancy mechanism of atomic migration. The relaxation times of the order parameters are derived for the homogeneous phase.