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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Master equation ： ウィキペディア英語版 Master equation In physics and chemistry and related fields, master equations are used to describe the time-evolution of a system that can be modelled as being in exactly one of the states at any given time, and where switching between states is treated probabilistically. The equations are usually a set of differential equations for the variation over time of the probabilities that the system occupies each of the different states. ==Introduction== A master equation is a phenomenological set of first-order differential equations describing the time evolution of (usually) the probability of a system to occupy each one of a discrete set of states with regard to a continuous time variable ''t''. The most familiar form of a master equation is a matrix form: :$\backslash frac=\backslash mathbf\backslash vec,$ where $\backslash vec$ is a column vector (where element ''i'' represents state ''i''), and $\backslash mathbf$ is the matrix of connections. The way connections among states are made determines the dimension of the problem; it is either *a d-dimensional system (where d is 1,2,3,...), where any state is connected with exactly its 2d nearest neighbors, or *a network, where every pair of states may have a connection (depending on the network's properties). When the connections are time-independent rate constants, the master equation represents a kinetic scheme, and the process is Markovian (any jumping time probability density function for state ''i'' is an exponential, with a rate equal to the value of the connection). When the connections depend on the actual time (i.e. matrix $\backslash mathbf$ depends on the time, $\backslash mathbf\backslash rightarrow\backslash mathbf(t)$ ), the process is not stationary and the master equation reads :$\backslash frac=\backslash mathbf(t)\backslash vec.$ When the connections represent multi exponential jumping time probability density functions, the process is semi-Markovian, and the equation of motion is an integro-differential equation termed the generalized master equation: :$\backslash frac=\; \backslash int^t\_0\; \backslash mathbf(t-\; \backslash tau\; )\backslash vec(\; \backslash tau\; )d\; \backslash tau\; .$ The matrix $\backslash mathbf$ can also represent birth and death, meaning that probability is injected (birth) or taken from (death) the system, where then, the process is not in equilibrium. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Master equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.