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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 GENERIC formalism ： ウィキペディア英語版 GENERIC formalism In non-equilibrium thermodynamics, GENERIC is an acronym for General Equation for Non-Equilibrium Reversible-Irreversible Coupling. It is the general form of dynamic equation for a system with both reversible and irreversible dynamics (generated by energy and entropy, respectively). GENERIC formalism is the theory built around the GENERIC equation, which has been proposed in its final form in 1997 by Miroslav Grmela and Hans Christian Öttinger. 〔 〕〔 〕〔 〕 ==GENERIC equation== The GENERIC equation is usually written as :$\backslash frac=L(x)\backslash cdot\backslash frac(x)+M(x)\backslash cdot\backslash frac(x).$ Here: * $x$ denotes a set of variables used to describe the state space. The vector $x$ can also contain variables depending on a continuous index like a temperature field. In general, $x$ is a function $S\backslash rightarrow\backslash mathbb\; R$, where the set $S$ can contain both discrete and continuous indexes. Example: $x=(U,V,T(\backslash vec\; r))$ for a gas with nonuniform temperature, contained in a volume $\backslash Sigma\backslash subset\backslash mathbb\; R^3$ ($S=\backslash \backslash cup\backslash Sigma$) * $E(x)$, $S(x)$ are the system's total energy and entropy. For purely discrete state variables, these are simply functions from $\backslash mathbb\; R^n$ to $\backslash mathbb\; R$, for continuously indexed $x$, they are functionals * $\backslash delta\; E/\backslash delta\; x$, $\backslash delta\; S/\backslash delta\; x$ are the derivatives of $E$ and $S$. In the discrete case, it is simply the gradient, for continuous variables, it is the functional derivative (a function $S\backslash rightarrow\backslash mathbb\; R$) * the Poisson matrix $L(x)$ is an antisymmetric matrix (possibly depending on the continuous indexes) describing the reversible dynamics of the system according to Hamiltonian mechanics. The related Poisson bracket fulfills the Jacobi identity.〔 〕 * the friction matrix $M(x)$ is a positive semidefinite (and hence symmetric) matrix describing the system's irreversible behaviour. In addition to the above equation and the properties of its constituents, systems that ought to be properly described by the GENERIC formalism are required to fulfill the degeneracy conditions :$L(x)\backslash cdot\backslash frac(x)=0$ :$M(x)\backslash cdot\backslash frac(x)=0$ which express the conservation of entropy under reversible dynamics and of energy under irreversible dynamics, respectively. The conditions on $L$ (antisymmetry and some others) express that the energy is reversibly conserved, and the condition on $M$ (positive semidefiniteness) express that the entropy is irreversibly non-decreasing. 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「GENERIC formalism」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.