非平衡热力学的极值定理 - 版本历史

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思无涯咿呀咿呀：/* References */

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References

Solitude：/* Fluctuations, entropy, 'thermodynamics forces', and reproducible dynamical structure */

2020-11-01T14:46:40Z

Fluctuations, entropy, 'thermodynamics forces', and reproducible dynamical structure

Solitude：/* Local thermodynamic equilibrium */

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Local thermodynamic equilibrium

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 ==参考文献==
+[[Category:待润色]]
 <noinclude>
 <small>This page was moved from [[wikipedia:en:Extremal principles in non-equilibrium thermodynamics]]. Its edit history can be viewed at [[非平衡热力学的极值定理/edithistory]]</small></noinclude>

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 It is pointed out by W.T. Grandy Jr that entropy, though it may be defined for a non-equilibrium system, is when strictly considered, only a macroscopic quantity that refers to the whole system, and is not a dynamical variable and in general does not act as a local potential that describes local physical forces. Under special circumstances, however, one can metaphorically think as if the thermal variables behaved like local physical forces. The approximation that constitutes classical irreversible thermodynamics is built on this metaphoric thinking.
-小W.T.格兰迪W.T. Grandy Jr 指出，熵虽然可以为非平衡系统定义，但严格考虑时，它只是一个宏观的量，指的是整个系统，并不是一个动态变量，一般情况下，它并不能作为描述局部物理力的局部势。但在特殊情况下，我们可以比喻为热变量的行为就像局部物理力一样。构成经典不可逆热力学的近似就是建立在这种隐喻思维的基础上。
+W.T.格兰迪(W.T. Grandy Jr) 指出，熵虽然可以为非平衡系统定义，但严格考虑时，它只是一个宏观的量，指的是整个系统，并不是一个动态变量，一般情况下，它并不能作为描述局部物理力的局部势。但在特殊情况下，我们可以比喻为热变量的行为就像局部物理力一样。构成经典不可逆热力学的近似就是建立在这种隐喻思维的基础上。
 As indicated by the " " marks of Onsager (1931),<ref name="Onsager 1931 I"/> such a metaphorical but not categorically mechanical force, the thermal "force", <math>X_{th}</math>, 'drives' the conduction of heat. For this so-called "thermodynamic force", we can write
-正如昂萨格Onsager(1931)的" "标记所表明的那样，<ref name="Onsager 1931 I"/>这样一个比喻性的但不是绝对的机械力，即热 "力"， <math>X_{th}</math>，"驱动 "着热量的传导。对于这个所谓的 "热力"，我们可以写为
+正如昂萨格Onsager(1931)的" "双引号标记所表明的那样，<ref name="Onsager 1931 I"/>这样一个比喻性的但不是绝对的机械力，即热 "力"， <math>X_{th}</math>，"驱动 "着热量的传导。对于这个所谓的 "热力"，我们可以写为
 :::::<math>X_{th} = - \frac{1}{T} \nabla T</math>.
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 Actually this thermal "thermodynamic force" is a manifestation of the degree of inexact specification of the microscopic initial conditions for the system, expressed in the thermodynamic variable known as temperature, <math>T</math>. Temperature is only one example, and all the thermodynamic macroscopic variables constitute inexact specifications of the initial conditions, and have their respective "thermodynamic forces". These inexactitudes of specification are the source of the apparent fluctuations that drive the generation of dynamical structure, of the very precise but still less than perfect reproducibility of non-equilibrium experiments, and of the place of entropy in thermodynamics. If one did not know of such inexactitude of specification, one might find the origin of the fluctuations mysterious. What is meant here by "inexactitude of specification" is not that the mean values of the macroscopic variables are inexactly specified, but that the use of macroscopic variables to describe processes that actually occur by the motions and interactions of microscopic objects such as molecules is necessarily lacking in the molecular detail of the processes, and is thus inexact. There are many microscopic states compatible with a single macroscopic state, but only the latter is specified, and that is specified exactly for the purposes of the theory.
-其实这种"热力学力"是系统微观初始条件不精确程度的一种表现，用被称为温度的热力学变量<math>T</math>表示。温度只是一个例子，所有的热力学宏观变量都构成了初始条件的不精确规格，都有各自的 "热力学力"。这些不精确的规格是推动动力结构产生明显波动的根源，是非平衡实验非常精确但仍不太完美的重复性的根源，也是熵在热力学中的地位的根源。如果不知道这种不精确的规格，人们可能会觉得波动的起源很神秘。这里所说的 "规格的不精确性"，并不是说宏观变量的均值规定得不精确，而是说用宏观变量来描述分子等微观物体的运动和相互作用实际发生的过程，必然缺乏过程的分子细节，因而不精确。有许多微观状态与单一的宏观状态相适应，但只有后者被规定，而这正是为了理论的目的而规定的。
+其实这种"热力学力"是系统微观初始条件不精确程度的一种表现，用被称为温度的热力学变量<math>T</math>表示。温度只是一个例子，所有的热力学宏观变量都构成了初始条件的不精确规格，都有各自的 "热力学力"。这些不精确的规格是推动动力结构产生明显波动的根源，是非平衡实验非常精确但仍不太完美的重复性的根源，也是熵在热力学中的地位的根源。如果不知道这种不精确的规格，人们可能会觉得波动的起源很神秘。这里所说的 "规格的不精确性"，并不是说宏观变量的均值规定得不精确，而是说用宏观变量来描述分子等微观物体的运动和相互作用实际发生的过程，必然缺乏过程的分子层面细节，因而不精确。有许多微观状态与单一的宏观状态相适应，但只有后者被规定，而这正是为了理论的目的而规定的。
 It is reproducibility in repeated observations that identifies dynamical structure in a system. [[Edwin Thompson Jaynes|E.T. Jaynes]]<ref name="Jaynes 1957 I">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics | url = http://bayes.wustl.edu/etj/articles/theory.1.pdf | journal = Physical Review | volume = 106 | issue = 4| pages = 620–630 | doi=10.1103/physrev.106.620| bibcode = 1957PhRv..106..620J }}</ref><ref name="Jaynes 1957 II">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics. II | url = http://bayes.wustl.edu/etj/articles/theory.2.pdf | journal = Physical Review | volume = 108 | issue = 2| pages = 171–190 | doi=10.1103/physrev.108.171| bibcode = 1957PhRv..108..171J }}</ref><ref name="Jaynes 1985">[http://bayes.wustl.edu/etj/articles/macroscopic.prediction.pdf Jaynes, E.T. (1985). Macroscopic prediction, in ''Complex Systems - Operational Approaches in Neurobiology'', edited by H. Haken, Springer-Verlag, Berlin, pp. 254-269] {{ISBN|3-540-15923-1}}.</ref><ref name="Jaynes 1965">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1965 | title = Gibbs vs Boltzmann Entropies | url = http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf | journal = American Journal of Physics | volume = 33 | issue = 5| pages = 391–398 | doi=10.1119/1.1971557| bibcode = 1965AmJPh..33..391J }}</ref> explains how this reproducibility is why entropy is so important in this topic: entropy is a measure of experimental reproducibility. The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result. When the process goes on in a system with less than a 'practically infinite' number (much much less than Avogadro's or Loschmidt's numbers) of molecules, the thermodynamic reproducibility fades, and fluctuations become easier to see.<ref name="Evans Searles 2002">{{cite journal | last1 = Evans | first1 = D.J. | last2 = Searles | first2 = D.J. | s2cid = 10308868 | year = 2002 | title = The fluctuation theorem | journal = Advances in Physics | volume = 51 | issue = 7| pages = 1529–1585 | doi=10.1080/00018730210155133| bibcode = 2002AdPhy..51.1529E }}</ref><ref name="WSMSE 2002">Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J., Evans, D.J. (2002) Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, ''Physical Review Letters'' 89: 050601-1 - 050601-4.</ref>

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 ==References==
 <noinclude>
 <small>This page was moved from [[wikipedia:en:Extremal principles in non-equilibrium thermodynamics]]. Its edit history can be viewed at [[非平衡热力学的极值定理/edithistory]]</small></noinclude>

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	==Fluctuations, entropy, 'thermodynamics forces', and reproducible dynamical structure==		==Fluctuations, entropy, 'thermodynamics forces', and reproducible dynamical structure==
		+
		+	波动，熵，“热力学力”和可重现的动力学结构

	Apparent 'fluctuations', which appear to arise when initial conditions are inexactly specified, are the drivers of the formation of non-equilibrium dynamical structures. There is no special force of nature involved in the generation of such fluctuations. Exact specification of initial conditions would require statements of the positions and velocities of all particles in the system, obviously not a remotely practical possibility for a macroscopic system. This is the nature of thermodynamic fluctuations. They cannot be predicted in particular by the scientist, but they are determined by the laws of nature and they are the singular causes of the natural development of dynamical structure.<ref name="G&P 1971"/>		Apparent 'fluctuations', which appear to arise when initial conditions are inexactly specified, are the drivers of the formation of non-equilibrium dynamical structures. There is no special force of nature involved in the generation of such fluctuations. Exact specification of initial conditions would require statements of the positions and velocities of all particles in the system, obviously not a remotely practical possibility for a macroscopic system. This is the nature of thermodynamic fluctuations. They cannot be predicted in particular by the scientist, but they are determined by the laws of nature and they are the singular causes of the natural development of dynamical structure.<ref name="G&P 1971"/>

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	==Local thermodynamic equilibrium==		==Local thermodynamic equilibrium==
		+
		+	局部热力学平衡

	Various principles have been proposed by diverse authors for over a century. According to Glansdorff and Prigogine (1971, page 15),<ref name="G&P 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London. {{ISBN\|0-471-30280-5}}</ref> in general, these principles apply only to systems that can be described by thermodynamical variables, in which [[Dissipative system\|dissipative processes]] dominate by excluding large deviations from statistical equilibrium. The thermodynamical variables are defined subject to the kinematical requirement of local thermodynamic equilibrium. This means that collisions between molecules are so frequent that chemical and radiative processes do not disrupt the local Maxwell-Boltzmann distribution of molecular velocities.		Various principles have been proposed by diverse authors for over a century. According to Glansdorff and Prigogine (1971, page 15),<ref name="G&P 1971">Glansdorff, P., Prigogine, I. (1971). ''Thermodynamic Theory of Structure, Stability and Fluctuations'', Wiley-Interscience, London. {{ISBN\|0-471-30280-5}}</ref> in general, these principles apply only to systems that can be described by thermodynamical variables, in which [[Dissipative system\|dissipative processes]] dominate by excluding large deviations from statistical equilibrium. The thermodynamical variables are defined subject to the kinematical requirement of local thermodynamic equilibrium. This means that collisions between molecules are so frequent that chemical and radiative processes do not disrupt the local Maxwell-Boltzmann distribution of molecular velocities.