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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 Adiabatic accessibility ： ウィキペディア英語版 Adiabatic accessibility Adiabatic accessibility denotes a certain relation between two equilibrium states of a thermodynamic system (or of different such systems). The concept was coined by Constantin Carathéodory〔Constantin Carathéodory: ''Untersuchungen über die Grundlagen der Thermodynamik'', Math. Ann., 67:355–386, 1909〕 in 1909 ("adiabatische Erreichbarkeit") and taken up 90 years later by Elliott Lieb and J. Yngvason in their axiomatic approach to the foundations of thermodynamics. It was also used by R. Giles in his 1964 monograph.〔Robin Giles: "Mathematical Foundations of Thermodynamics", Pergamon, Oxford 1964〕 A system in a state ''Y'' is said to be adiabatically accessible from a state ''X'' if ''X'' can be transformed into ''Y'' without the system suffering transfer of energy as heat or transfer of matter. ''X'' may, however, be transformed to ''Y'' by doing work on ''X''. For example, a system consisting of one kilogram of warm water is adiabatically accessible from a system consisting of one kilogram of cool water, since the cool water may be mechanically stirred to warm it. However, the cool water is not adiabatically accessible from the warm water, since no amount or type of work may be done to cool it. The original definition of Carathéodory was limited to reversible, quasistatic process, described by a curve in the manifold of equilibrium states of the system under consideration. He called such a state change adiabatic if the infinitesimal 'heat' differential form $\backslash delta\; Q=dU-\backslash sum\; p\_idV\_i$ vanishes along the curve. In other words, at no time in the process does heat enter or leave the system. Carathéodory's formulation of the Second Law of Thermodynamics then takes the form: "In the neighbourhood of any initial state, there are states which cannot be approached arbitrarily close through adiabatic changes of state." From this principle he derived the existence of entropy as a state function $S$ whose differential $dS$ is proportional to the heat differential form $\backslash delta\; Q$, so it remains constant under adiabatic state changes (in Carathéodory's sense). The increase of entropy during irreversible processes is not obvious in this formulation, without further assumptions. The definition employed by Lieb and Yngvason is rather different since the state changes considered can be the result of arbitrarily complicated, possibly violent, irreversible processes and there is no mention of 'heat' or differential forms. In the example of the water given above, if the stirring is done slowly, the transition from cool water to warm water will be quasistatic. However, a system containing an exploded firecracker is adiabatically accessible from a system containing an unexploded firecracker (but not vice versa), and this transition is far from quasistatic. Lieb and Yngvason's definition of adiabatic accessibility is: A state $Y$ is adiabatically accessible from a state $X$, in symbols $X\backslash prec\; Y$, if it is possible to transform $X$ into $Y$ in such a way that the only net effect of the process on the surroundings is that a weight has been raised or lowered (or a spring is stretched/compressed, or a flywheel is set in motion). A definition of thermodynamic entropy can be based entirely on certain properties of the relation $\backslash prec$ of adiabatic accessibility that are taken as axioms in the Lieb-Yngvason approach. In the following list of properties of the $\backslash prec$ operator, a system is represented by a capital letter, e.g. ''X'', ''Y'' or ''Z''. A system ''X'' whose extensive parameters are multiplied by $\backslash lambda$ is written $\backslash lambda\; X$. (e.g. for a simple gas, this would mean twice the amount of gas in twice the volume, at the same pressure.) A system consisting of two subsystems ''X'' and ''Y'' is written (X,Y). If $X\; \backslash prec\; Y$ and $Y\; \backslash prec\; X$ are both true, then each system can access the other and the transformation taking one into the other is reversible. This is an equivalence relationship written $X\; \backslash overset\}\; Y$. Otherwise, it is irreversible. Adiabatic accessibility has the following properties:〔 *Reflexivity: $X\; \backslash overset\}\; X$ *Transitivity: If $X\; \backslash prec\; Y$ and $Y\; \backslash prec\; Z$ then $X\; \backslash prec\; Z$ *Consistency: if $X\; \backslash prec\; X\text{'}$ and $Y\; \backslash prec\; Y\text{'}$ then $(X,Y)\; \backslash prec\; (X\text{'},Y\text{'})$ *Scaling Invariance: if $\backslash lambda\; >\; 0$ and $X\; \backslash prec\; Y$ then $\backslash lambda\; X\; \backslash prec\; \backslash lambda\; Y$ *Splitting and Recombination: $X\backslash overset\}((1-\backslash lambda)X,\backslash lambda\; X)$ for all *Stability: if $\backslash lim\_\; (Z\_0)\; \backslash prec\; (Y,\backslash epsilon\; Z\_1))$ then $X\; \backslash prec\; Y$ The entropy has the property that $S(X)\backslash leq\; S(Y)$ if and only if $X\backslash prec\; Y$ and $S(X)=\; S(Y)$ if and only if $X\; \backslash overset\}\; Y$ in accord with the Second Law. If we choose two states $X\_0$ and $X\_1$ such that $X\_0\; \backslash prec\; X\_1$ and assign entropies 0 and 1 respectively to them, then the entropy of a state ''X'' where $X\_0\; \backslash prec\; X\; \backslash prec\; X\_1$ is defined as:〔 :$S(X)\; =\; \backslash sup\; (\backslash lambda\; :\; ((1-\backslash lambda)X\_0,\; \backslash lambda\; X\_1)\; \backslash prec\; X)$ ==Sources== 〔 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「Adiabatic accessibility」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.